Aguero has scored 154 goals for the Blues, now trailing only Tommy Johnson (166) and Eric Brook (178).
Guardiola's first taste of the FA Cup as a manager finished triumphantly as his Manchester City side whipped West Ham in the third round. City drove 3-0 at the break, Yaya Toure beginning the defeat by terminating a far from being obviously true penalty into the left corner. Havard Nordtveit packaged Bacary Sagna's prodding cross into his own net, only 146 seconds before David Silva's well composed tap-in.
Soon after the restart, Sergio Aguero brazenly occupied in Toure's shot to end up distinctly the third-most elevated goalscorer in City's history. Also, John Stones headed in his first Blues goal as the guests easily observed the game out in a quickly emptying London Stadium. Taking after Friday's opening third-round tie, City are the first team in the pot for Monday's draw.
More on West Ham vs. Man City
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But the hosts improved after the break as Gael Clichy squeezed home a shot before Sergio Aguero, on as a substitute, fired home from a tight angle.
Ben Mee smashed home via the underside of the bar shortly after but Burnley could not force a leveller despite a fine chance for Andre Gray late on.
Match Highlights
City take the hard road
Beginning the day 10 points behind leaders Chelsea, anything less than victory would have prompted some to begin reading the last rites on City's title challenge.
As it is, Pep Guardiola's side will look at the league table with renewed optimism as they closed to within four points of second-place Liverpool with one and possibly both of Chelsea and Tottenham to drop points when they face each other on Wednesday.
However, Fernandinho's dismissal meant they had to fight harder than they might have expected for victory.
The City captain took some of the ball as he contested a 50:50 ball in midfield, but his reckless scissor-action style meant that Lee Mason's could easily justify his decision to show red.
It is not the first time City's discipline has hindered their title ambitions. Including Sergio Aguero's retrospective red against West Ham, they have been shown seven red cards in Guardiola's 30 games in charge.
⚽ Liverpool beat Man City thanks to Wijnaldum goal
Georginio Wijnaldum's header was the difference in a game of few clear chances
Liverpool maintained their pursuit of Premier League leaders Chelsea as they moved to within six points of the pacesetters with victory over Manchester City at Anfield.
Georginio Wijnaldum's soaring eighth-minute header from Adam Lallana's cross was enough to put Liverpool in second place and put a serious dent in City's own title challenge.
Liverpool manager Jurgen Klopp led the celebrations at the end of a game that was high on energy but sadly lacking in any moments of genuine quality.
City, who laboured throughout, improved in the second half but never seriously threatened Liverpool goalkeeper Simon Mignolet and this loss leaves them 10 points adrift of Chelsea.
Klopp gets better of Pep.
Jurgen Klopp and Pep Guardiola were meeting for the first time in England
This was the first Premier League meeting between two huge personalities straight from the top tier of management - and it brought a victory for Jurgen Klopp to cherish at Pep Guardiola's expense.
The head-to-head was locked at 4-4 after their meetings in Germany with Borussia Dortmund and Bayern Munich. This was a different stage with different prizes on offer - but it was an occasion that was just as charged.
Klopp, in 15 months, has revitalised Liverpool and given hope to supporters longing to end the wait for a first title since 1990. And as they continue their pursuit of relentless Chelsea, belief continues to grow that the charismatic German can still haul in Antonio Conte's side.
Liverpool's manager was, as usual, celebrating with his players after the final whistle before pumping his chest in mock relief in front of Anfield's huge new Main Stand.
And, when City fleetingly threatened a second-half comeback, he turned cheerleader in front of those same fans with a demand to lift the noise levels that was met instantly.
Klopp has become the new Anfield talisman. Under him, the transformation of his team and the mood around the club continues.
Something else that will give Liverpool's fans great heart is the way in which Klopp is getting results against his closest rivals.
Since his appointment in October 2015, Klopp has faced a total of 13 Premier League games against Arsenal, Chelsea, Manchester City, Manchester United and Tottenham. He has lost only one - a single goal defeat by United last season.
He has also enjoyed a Europa League win over two legs against United, although the balance is redressed slightly by a loss on penalties against Manchester City in last season's Capital One Cup final.
Man of the match - Georginio Wijnaldum
Georginio Wijnaldum's header was the difference in a game of few clear chances
What they said
Liverpool manager Jurgen Klopp: "I know everyone talks about our defence. It's not about avoiding goals - that's the end product - it's about how we work together.
"I think we have the smallest number of shots on our goal in the league. Tonight the concentration level was outstanding.
"I don't care about criticism of our defence. You always pick out things that aren't right but that's how goals are."
Manchester City boss Pep Guardiola: "It was an equal game. The goal made it difficult against a team who use the counter-attack like a master. The second half was much better.
"We have to wake up for another game. We need to focus and work - we can't think about the big goals."
What's next?
A swift turnaround. City host Burnley at 15:00 GMT on Monday, while at the same time Liverpool are at struggling Sunderland.
Yaya Toure has scored all 10 of his Premier League penalty kicks
Manchester City climbed to second place in the Premier League with a workmanlike victory over bottom side Hull City at the KCOM stadium.
Pep Guardiola's visitors were far from their free-flowing best en route to their 12th win of the season, but were nevertheless good value for a win that keeps them seven points behind leaders Chelsea.
Yaya Toure's penalty, awarded after Andrew Robertson's clumsy challenge on Raheem Sterling, set the visitors on their way before Kelechi Iheanacho added a second from close range and Curtis Davies conceded an own goal in the dying seconds.
Hull have now conceded nine penalties so far in the league this season - four more than any other side.
The hosts played well in patches and saw Michael Dawson's second-half header cleared off the line by Bacary Sagna, but their return of one win in 16 matches is a damning statistic that points to only one outcome come season's end.
And it will not be lost on Tigers fans that the side bottom on Christmas Day have only stayed up three times in the 24 Premier League seasons to date.
Hull City vs Manchester City: Live Score and Stats.
Manchester City moved up to second in the Premier League table as Arsenal squandered a lead to lose for the second successive game.
Theo Walcott's cool fifth-minute finish from Alexis Sanchez's pass put the Gunners in control at the interval - but the second half brought a familiar painful fate for manager Arsene Wenger and his players.
As at Everton on Tuesday, they were overpowered and the credits were rolling once Leroy Sane ran on to David Silva's pass to beat Petr Cech with Arsenal appealing in vain for offside.
EPL Table As It Stands
See The Full Premier League Table Here. City were on a roll and Arsenal were on the rack, the winner coming 19 minutes from time when Raheem Sterling was the beneficiary of Kevin De Bruyne's brilliant pass to arrow a low finish past Cech at his near post.
It bolstered City's title ambitions, although they are still seven points behind leaders Chelsea and completed a damaging double for Arsenal as they now lie nine points behind Antonio Conte's side.
De Bruyne steps up as Ozil disappears
Manchester City needed their main man when they trailed at half-time - and in the absence of the suspended Sergio Aguero that role is assumed by De Bruyne.
And how the Belgian responded, delivering a virtuoso second-half performance crowned by that superb pass that led to Sterling's winner.
De Bruyne was the driving force behind City's second-half transformation that saw Pep Guardiola's team wrestle control from Arsenal with a change of tempo and intensity that was simply too much for Arsenal to resist.
The same could not be said for Arsenal's elite players and the main culprit was Mesut Ozil who, as in the fierce atmosphere of Goodison Park on Tuesday, shrank from the occasion and wandered around aimlessly and ineffectively on the game's periphery.
Ozil is in the middle of what are likely to be very lucrative contract negotiations. Performances like this will diminish his hand in the bargaining rather than strengthen it.
Good week for Guardiola and Man City... Manchester City and Guardiola knew a lot was riding on two home games this week after the result, and the manner of the 4-2 defeat at Leicester City last Saturday.
City simply had to beat Watford and Arsenal, the stakes even higher after Chelsea stretched their lead to nine points with victory at Crystal Palace on Saturday.
A draw was no use to either side here - so the notion of defeat was even more unpalatable.
City were on the brink as they were behind at half-time but Guardiola responded by sending on Bacary Sagna for Pablo Zabaleta and Sane, who had been out on the wing, was soon racing through to score from a central position.
It was a win City needed desperately and its importance was illustrated by the celebrations at the final whistle.
...bad week for Wenger and Arsenal
Just when some of the old doubts about Arsenal's resilience and resistance to pressure seemed to be receding, all the familiar questions will return after the way they have lost a lead and slumped to defeat at Everton and now at Manchester City.
Arsenal looked in calm control holding the advantage on both occasions but have twice found themselves broken by physical presence and the greater intensity of opponents who were simply prepared to dig deeper.
Wenger was wearing a familiar frustrated expression at the final whistle.
And at the back of many Arsenal minds will be the familiar tales and pain of previous seasons when promise and potential ended in title under-achievement.
Pep Guardiola may well have envisaged life in England being tougher than he was used to in Munich — but he probably didn't expect to go as badly as it has over the last few months. Manchester City have now won just four of their last 15 matches in all competitions. They were treated to a 4-2 hammering at home to Leicester last weekend and are fourth in the Premier League.
Walter Mazzarri's Watford, meanwhile, have been defying expectations this season. The Hornets are ninth in the table and have beaten both Everton and champions Leicester in recent weeks.
Regardless of form, the travelling fans are unlikely to be expecting a win tonight. They could certainly get something from this game, though.
Toure has scored twice in five appearances for Manchester City this season
Manchester City midfielder Yaya Toure has pleaded guilty to drink-driving, but says he had not "intentionally consumed alcohol".
The Ivory Coast player, 33, told a court he thought he was drinking diet cola from a jug at a party, without realising it had brandy in it.
Toure did not challenge the charge as he was "above the permitted limit".
He was fined £54,000 - a means-tested fine - and banned from driving for 18 months by Barkingside magistrates.
"It is well known that I am a Muslim and do not drink, said Toure. "I have always refused alcohol."
Toure was driving in Dagenham in east London at the time of the offence last month.
Barkingside Magistrates Court said Toure had an alcohol reading of 75 micrograms per 100 millilitres of breath - more than twice England's legal limit of 35 micrograms.
He pleaded guilty to the charge on Monday, but did not say in his Facebook statement how the alcohol got into his system.
In his statement Toure added: "Drink-driving is a serious crime and even though I was not intentionally consuming alcohol I accept the ban and fine and I would like to apologise for this situation."
The Ivory Coast international was recalled to the Manchester City squad earlier this month after apologising for "misunderstandings" relating to comments made by his agent Dimitri Seluk.
Jamie Vardy scored his first hat-trick since his three goals for Fleetwood against Ebbsfleet on 21 February 2012
Jamie Vardy scored a hat-trick as Leicester City pulled off a stunning victory over an out-of-sorts Manchester City.
The Foxes were 2-0 up in five minutes as Vardy ended his 10-game run without a Premier League goal by slotting home, and Andy King curled in moments later.
It was 3-0 within 20 minutes as Vardy added another after skipping past visiting keeper Claudio Bravo, and he completed his hat-trick by intercepting a misplaced John Stones pass and finishing from a narrow angle.
Aleksandar Kolarov, with a free-kick, and Nolito scored late consolation goals for the away side.
They have now lost back-to-back league games for the first time since Pep Guardiola took over in the summer, and are four points adrift of leaders Arsenal.
For defending champions Leicester, victory ended a five-game run without a league win and moved them up to 14th.
Guardiola said this week he wanted a new rule to allow teams to use up to six substitutes - and after five minutes he may have hoped his wish was a reality.
Manchester City have kept just two Premier League clean sheets this season, and Guardiola reshuffled his formation to start with a back three of Pablo Zabaleta, John Stones and Bacary Sagna.
That strategy was swiftly scrapped, though, when his side fell 2-0 down after just 255 seconds - Kolarov was hauled out of midfield and into a hastily created back four.
The visitors, looking marginally better for the change, still managed to get caught on the break for Leicester's third and frequently put themselves under pressure by trying to play out from the back - Stones' misplaced backpass for Vardy's third the costliest example.
Their fragility could well be a result of their lack of a consistent starting XI, with Guardiola never having kept the same line-up for two consecutive games during his time at Etihad Stadium.
Suspensions for Sergio Aguero, Fernandinho and Nicolas Otamendi had forced the Spaniard to make changes here, and his side were devoid of cohesion.
For all their possession, they did not have their first shot on target until Kolarov scored a well-placed free-kick in the 82nd minute, and only salvaged further respectability when Nolito tapped in the Serb's low cross late on.
Man of the match - Jamie Vardy
A first hat-trick for Leicester in a performance reminiscent of his best displays last season - the confidence poured back into him after his first goal
What They Said
Leicester boss Claudio Ranieri told BBC Sport: "It was the true Leicester, maybe because we have played so badly in our last few matches, but today we were so strong.
"We played smart, slowed down the tempo.
"I am very pleased for Jamie. When he finished, I said 'welcome back'."
Manchester City boss Pep Guardiola told BBC Sport: "Leicester won the second balls and scored fantastic goals.
"Football is a game with mistakes, especially today. I would never complain to my players and I will look inside myself and analyse the reason why we have problems with the second balls when they arrive.
"Our game is not bad, but in the box we have a lot of problems."
What's next?
On Monday, both sides find out who they will face in the last 16 of the Champions League.
Manchester City will be drawn against one of Atletico Madrid, Borussia Dortmund, Juventus, Monaco or Napoli.
Leicester City will meet Bayer Leverkusen, Bayern Munich, Benfica, Paris St-Germain, Real Madrid or Sevilla.
On Tuesday, Leicester travel to Bournemouth (19:45 GMT). Manchester City host Watford the following day (20:00).
Kelechi Iheanacho equalises for Manchester City (REUTERS)
Pep Guardiola wanted to get a good look at his young Manchester City players last night, although it ended up being one on the opposite side who will have caught his eye.
Patrick Roberts has been on loan at Celtic since January after joining City from Fulham the previous summer in a projected £11 million transfer. It is somewhat ironic that his first start at the Etihad Stadium should come against his parent club but the England Under-20 winger needed just four minutes to show Guardiola what he is all about. If Roberts is angling for a move back to City next summer, a fine run and finish was not a bad way to go about things.
In fact, it was a good night all round for City’s young slickers, with Kelechi Iheanacho cancelling out Roberts’s strike with a rather classy one of his own to provide a timely reminder to Guardiola of his talents with Sergio Agüero ruled out of the next four Premier League matches through suspension.
MATCH HIGHLIGHT
If this was a chance for Guardiola to give some of his youngsters an airing, it was also a welcome opportunity for the City manager to rest his star names ahead of the visit to champions Leicester City on Saturday evening. Leroy Sané was the only survivor from the side that started against Chelsea at the weekend, and while one of those 10 changes was enforced with Fernandinho suspended after his dismissal in the previous Champions League match against Borussia Mönchengladbach, Iheanacho was given the nod here over Agüero. Celtic had taken an early lead at Parkhead in that thrilling 3-3 draw in September and it was the same again here as City were caught napping. Sané could not control a poor pass out by goalkeeper Willy Caballero, Celtic intercepted, Roberts collected possession and set off inside, sweeping past Gaël Clichy before curling a shot into the far corner, albeit with a slight deflection off Tosin Adarabioyo.
Four minutes later and City were level. Ilkay Gündogan fed Nolito, who thread a ball through for Iheanacho to chase. Surging away from the lumbering figure of Jozo Simunovic, Iheanacho fired nonchalantly into the top corner.
It was not shaping up to be a good night for defenders with both sides getting behind each other far too easily. Nolito found Pablo Zabaleta, reinventing himself here as a maraudering box-to-box midfielder, with a wonderful first time pass. Zabaleta’s measured pass into the path of Iheanacho was a peach, too, and really deserved better than to be sliced horribly wide.
That said, Moussa Dembélé should also have done better when slipped in by James Forrest after the Celtic winger had floated past three City defenders with embarrassing ease. These were tough beginnings for Adarabioyo, making his first start in the Champions League for City. He had hurt himself early on when he landed awkwardly after challenging Dembélé for the ball and his movement was briefly restricted afterwards, which helped to explain how Dembélé evaded his attentions only to be wrongly ruled offside as he forced a save from Caballero. Iheanacho was later denied with a back-heel from close range. It was a chaotic if lively affair.Both teams had chances to win it in the second half. Nolito found the net but was ruled offside from Jesus Navas’s cross, Sané flashed a free-kick wide and was also denied at close range while Leigh Griffiths, Mikael Lustig and Gary Mackay-Steven all spurned inviting chances for Celtic.
Atletico Madrid, Napoli and Monaco are among the guaranteed group winners City could face in the Champions League Round of 16 but they will be spared a meeting with Bayern Munich or Paris St-Germain who, like them, both finished as runners-up in their respective groups.
Chelsea's eighth successive Premier League win cemented their place at the top of the table - but their victory at Etihad Stadium ended in chaos as Manchester City's Sergio Aguero and Fernandinho were sent off in injury time.
Antonio Conte's side delivered an impressive statement of intent as they cut City apart on the break after going behind to Gary Cahill's own goal on the stroke of half-time, when he diverted Jesus Navas's cross beyond Thibaut Courtois.
The game turned on Kevin De Bruyne's 56th minute miss with City in control, crashing Navas's cross against the bar from inside the six-yard area.
Chelsea were level on the hour when Diego Costa outmuscled Nicolas Otamendi to score and they were ahead ten minutes later when substitute Willian raced clear to beat City keeper Claudio Bravo with ease.
Eden Hazard completed a magnificent win for Chelsea with another goal on the break, showing too much pace for Aleksandar Kolarov to wrap up three vital points.
Chelsea's renaissance since their 3-0 loss at Arsenal left them in 10th place eight points behind then leaders City has been hugely impressive - but this is their most powerful statement of the season.
Eight wins from eight and only two goals conceded tells the story and this win against City was the second week in succession they have come from behind to beat a team that could be regarded as realistic title rivals after overcoming Tottenham at Stamford Bridge last weekend.
They were tested here by periods of City domination but showed a ruthlessness to match their steely resilience to tear Pep Guardiola's side to shreds in the closing 20 minutes.
Conte's switch to a three-man defensive system and the rejuvenation of key men such as Costa and Hazard is making this Chelsea side resemble the full title package.
Guardiola's defensive chaos
Manchester City have kept one clean sheet at home in the Premier League this season - in the 4-0 win against Bournemouth - and on this evidence it is easy to see why.
For all City's domination of possession and creation, Guardiola's side have an Achilles heel at the back that was ruthlessly exposed here.
Yes, Kevin De Bruyne should have put the game out of Chelsea's reach but City defence offered the visitors hope throughout and how they capitalised when given the chance.
Guardiola has been linked with defensive reinforcements, particularly Southampton's Virgil van Dijk, and the manner in which they were dismantled here now makes this a matter of urgency.
The jitters started early when John Stones was caught in possession in his own area, while defensive partner Nicolas Otamendi had a nightmare afternoon and was culpable for Chelsea's first two goals from Costa, where he was weak in the challenge, and Willian.
Guardiola gestured in despair towards his central defenders after Willian's goal - his displeasure will surely take the form of more decisive action in January.
An unsavoury end
It is unlikely either Manchester City or Chelsea have heard the last of a shameful conclusion to a high-class game of football as players and officials from both sides became embroiled in ugly scenes.
City's frustration at what they believed were a series of injustices at the hands of referee Anthony Taylor boiled over injury time as Aguero caught Luiz high and late, which happened after the Argentine clashed with the defender at a corner earlier.
Chelsea's Nathaniel Chalobah joined in and was lucky not to see red as a crowd scene developed on the touchline as Fernandinho was sent off for grabbing Fabregas.
Even then, Fernandinho had to be forced to leave the pitch and with the whole situation threatening to go completely out of control, it was fortunate referee Taylor was able to blow the final whistle seconds later.
Gary Cahill's own goal in first half injury time gave Manchester City the half-time lead
It is hard to see how both clubs can escape censure for a failure to control their players.
Man of the match: Eden Hazard (Chelsea)Chelsea's eighth successive Premier League win cemented their place at the top of the table - but their victory at Etihad Stadium ended in chaos as Manchester City's Sergio Aguero and Fernandinho were sent off in injury time.
