Sunderland equalised six minutes later as Defoe scored from the spot following Ragnar Klavan's trip on Didier Ndong, before Sadio Mane put the visitors back ahead with a close-range finish.
However, Mane then handled in his own 18-yard box and Defoe converted the penalty to snatch an unlikely point.
Match Highlights
Liverpool's missed opportunity
The result leaves Liverpool five points behind Premier League leaders Chelsea, who play their game in hand on Wednesday at Tottenham (20:00 GMT kick-off).
However, Reds boss Jurgen Klopp will surely see it as two points dropped after his side led twice, had 71% of the possession and had 15 shots on target.
Only an inspired performance from Black Cats keeper Vito Mannone denied Liverpool further goals, before Mane needlessly stuck out an arm to block Seb Larsson's free-kick, costing his side dearly.
To make things worse for Liverpool, Sturridge, who scored only his second Premier League goal of the season, limped off late on after clashing with Papy Djilobodji.
Manchester United recorded their fourth successive Premier League win with a dominant performance against a Sunderland side which remains in the relegation zone.
United deserved the victory - enjoying 63% of possession and having a total of 25 shots on goal - but only a first-half Daley Blind effort separated the teams until the final 10 minutes.
The Dutchman was put through by a delightful Zlatan Ibrahimovic pass and fired low into the bottom-right corner for his first goal of the season, before United doubled their advantage with Paul Pogba setting up Ibrahimovic with eight minutes remaining.
Substitute Henrikh Mkhitaryan added gloss to the scoreline with a brilliant backheeled effort, though replays suggested the Armenian was offside.
It is a victory which draws United level with fifth-placed Tottenham, although the north Londoners have a game in hand, against Southampton on Wednesday.
Fabio Borini scored a wonderful late consolation for Sunderland, but defeat - their third in four games - leaves the Black Cats two points adrift of safety.
United find their groove
Both halves belonged to the hosts and the passing statistics emphasised their dominance, with Jose Mourinho's men making 606 passes compared to Sunderland's 177.
But the hosts were unable to shake off the visitors until the introduction of Mkhitaryan after the break added much-needed zip and verve.
Pogba was the dominant player on the pitch, bossing play from the middle of the field and driving his team forward, and while Ibrahimovic played a part in all three goals it was Mkhitaryan who gave his side an extra dimension in attack.
The 27-year-old's strike was a special one, with the former Borussia Dortmund player directing Ibrahimovic's cross into net with the back of his heel.
"It's a pity it was the third goal of the game, not one that won the match because that would've been in Man United history," said Mourinho, who admitted his team were lucky to be ahead in the first half.
"He played for 25 minutes and played well and he's doing great things," added the United manager of the club's summer signing who is now impressing after initially struggling to make an impact.
Cesc Fabregas has scored more goals against Sunderland (five) than against any other Premier League team
Chelsea moved six points clear at the top of the Premier League as Cesc Fabregas' first-half goal beat a stubborn Sunderland at the Stadium of Light. The Spain international hit before half time to break the Black Cats' resolve, as Antonio Conte's men kept a firm hold on the Premier League summit Cesc Fabregas scored the only goal as Chelsea won at Sunderland to secure a 10th successive top-flight victory and a six-point lead at the top of the Premier League.
Antonio Conte's side took full advantage of Arsenal's 2-1 loss at Everton on Tuesday to secure a firm grip on pole position, Fabregas netting the decisive goal after 40 minutes against a largely toothless Sunderland, although Thibaut Courtois was called upon to make a stunning injury-time save from Patrick van Aanholt to preserve the visitors' advantage.
Chelsea's position contrasts starkly to that which they held exactly one year ago, when a 2-1 defeat away at Leicester City left them one point clear of the relegation zone after 16 matches and proved to be the final game in Jose Mourinho's second stint in charge.
Sunderland were guilty of sitting deep and letting the Blues dictate terms, Fabregas finally making the breakthrough in a tepid first half when he steered a pass from Willian – making his first Premier League start since October 1 with Eden Hazard absent through injury – past Jordan Pickford.
David Moyes' team lacked coherency in attack and, after Adnan Januzaj was denied by Courtois, only the crossbar stopped them slipping further behind to Willian's deflected shot in the 51st minute.
Pickford kept the in-form Diego Costa at bay but Chelsea had done enough to continue their exemplary run of form, while Sunderland remain rooted to the bottom.
Chelsea dominated possession in the first half but struggled to break down a well-organised Sunderland defence, though the hosts were unable to keep hold of the ball when they won it back.
A rare foray forward from Moyes' team ended with Januzaj failing to get enough bend on an 18-yard effort to pick out the top-left corner after 25 minutes.
Chelsea responded with a swift break down the left that saw Marcos Alonso's drilled delivery find Costa, who was unable to cope with the pace on the ball and skewed a volley wide.
Conte's team continued to control proceedings and finally broke through five minutes before half-time when Billy Jones' stray header on the halfway line was pounced upon by N'Golo Kante, enabling Chelsea to surge forward with Willian teeing up Fabregas to guide home from the edge of the box.
Willian was unable to get enough dip on a free-kick from just outside the area in order to test Pickford in first-half stoppage time.
Januzaj was denied by an excellent near-post save from Courtois within two minutes of the restart, but it proved to be a flash in the pan for Sunderland.
Willian's attempt from the right-hand side of the box deflected off ex-Chelsea defender Papy Djilobodji and hit the bar on its way behind, while Pickford got a strong pair of hands down to his left to keep out Costa in the 53rd minute.
Jones was replaced by Donald Love after sustaining an injury in the 59th minute but Sunderland were unable to stem the flow with efforts from Victor Moses and Willian flying wide of the target.
Having spent most of the evening on the back foot, Sunderland almost conjured up an equaliser in the 93rd minute, Courtois springing to his right to palm a swerving effort from former Chelsea man Van Aanholt around the post.
Liverpool are 14 games unbeaten in all competitions
Liverpool moved back to the top of the Premier League with a win against Sunderland but could face a run of games without Philippe Coutinho who was taken off on a stretcher at Anfield.
The Brazillian clutched his ankle after a challenge from Didier Ndong late in a first half where Liverpool failed to turn 80% possession into clear chances.
Sunderland threatened briefly in each period, with Steven Pienaar and Duncan Watmore taking heavy touches when presented with openings.
But as Jurgen Klopp's side continued to press, it was Coutinho's replacement, Divock Origi, who found the net with what appeared to be a right-foot cross from the left side of the area.
It sparked relief at Anfield and when Ndong felled Sadio Mane in the box, James Milner converted a spot-kick to make it 14 games unbeaten in all competitions for the Reds.
How Liverpool deal with a potential lay-off for Coutinho will be critical in whether their momentum can lead to a push for an elusive Premier League title.
His contribution of five goals and six assists in the league sums up the key role he has under Klopp and his all-round displays have seen reports of interest from Barcelona.
Against David Moyes' side Coutinho seemed to be man-marked early on. When he escaped the attentions of Jason Denayer after half an hour he took a heavy touch in the area and felt the full force of Ndong's clearance.
There was no suggestion of a foul but Coutinho's foot took the impact of both the ball and Ndong's follow-through, and he instantly waved to the bench before grimacing during treatment.
Philippe Coutinho instantly grabbed his foot after Ndong's challenge
Origi's impact points to Liverpool having the resources to deal with any spell out for Coutinho. But with Sadio Mane primed to attend the African Cup of Nations with Senegal in January, Klopp will desperately hope he has not lost arguably his most creative force for long.
Sanchez took his tally to eight goals this season with his double at Sunderland
Arsenal increased the pressure on Sunderland manager David Moyes with a comfortable victory over a Black Cats side who remain bottom of the table and without a Premier League win this season.
Alexis Sanchez put the Gunners ahead when he got in front of defender Lamine Kone to head in Alex Oxlade-Chamberlain's cross.
The dominant visitors had a strong penalty appeal turned down after Sanchez looked to have been brought down before Jermain Defoe equalised from the spot after keeper Petr Cech had fouled Duncan Watmore.
Manchester City 2-1 Sunderland Agüero (4' minutes pen), McNair (87' minutes og FT Defoe (71' minutes)
Venue: Etihad Stadium LIVE Stream: Is Closed
EPL Table
Pep Guardiola needed a late Paddy McNair own goal to make a winning start at Manchester City as David Moyes lost his first game as Sunderland manager.
Sergio Aguero's penalty, after Raheem Sterling was fouled by Patrick van Aanholt, gave City an early lead.
But Guardiola, who left England keeper Joe Hart out of his starting XI, saw his new side concede to Jermain Defoe.
City made few chances, but snatched an 87th-minute winner when McNair put into his own net.
Pep's side need more punch
It had been 195 days since City announced Guardiola would succeed Manuel Pellegrini at Etihad Stadium, and results stagnated during that period, with five wins from last season's final 15 Premier League games leading to a fourth-placed finish.
Guardiola, 45, comes to Manchester with six league championships to his name - three each from his spells at Barcelona and Bayern Munich - and with his arrival comes an expectation he will guide City to a first Premier League title since 2014.
But any hopes of an instant revolution at City were curtailed by a lethargic performance that lacked creative spark, despite dominating possession against a side that only avoided relegation in their penultimate game last season.
And while City may have required good fortune for the decisive goal - McNair heading in Jesus Navas' cross at the back post - it provides a winning platform for Guardiola, who was lacking injured first-team players Vincent Kompany, Samir Nasri, Nicolas Otamendi and new signing Leroy Sane.
WATCH All Goals & Highlights ~ Sunderland 2-1 Manchester United ~ 13/2/2016 [Premier League]
Sunderland boosted their Premier League survival hopes with a deserved victory over an uninspired Manchester United.
Wahbi Khazri put the strugglers ahead after three minutes with a free-kick from the left that eluded everyone.
Anthony Martial levelled after he clipped the ball over Vito Mannone, who had parried Juan Mata's shot.
But the Black Cats won it when Lamine Kone's header from Khazri's corner went in via a deflection off David de Gea to dent United's top-four bid.
Will Allardyce's signings keep Sunderland up?
Wahbi Khazri was one of four Sunderland signings in January
Sunderland's win takes them to within one point of rivals Newcastle and safety after a game inspired by manager Sam Allardyce's January signings.
Tunisia forward Khazri made his first Premier League start in their last game, a 2-2 draw with Liverpool where he assisted Jermain Defoe's equaliser.
And the signing from Bordeaux was inspired again, scoring early on against United with a free-kick which Defoe stepped over to bamboozle United's defence and De Gea.
And their winner - while credited as a De Gea own goal - was all thanks to the powerful header from Kone, a signing from Lorient.
De Gea got a touch, with Martial appearing to hit the ball off his own keeper on the way in.
Allardyce told BBC MOTD: "The new players have been on the list before January. The problem is can you get them here and do they want to come and join the fight? They were desperate to come here."
Pressure will not ease on Van Gaal
We can only blame ourselves - Van Gaal
Manchester United boss Louis van Gaal has been frustrated this week by media reports, including from BBC Sport, saying that Jose Mourinho's representatives have spoken to the club about their client replacing the Dutchman.
Van Gaal had continued to insist that the club can finish in the top four, although the defeat keeps fifth-placed United six points behind Manchester City, who now have a game in hand.
And, after the game, Van Gaal said it will be "very difficult" for them to qualify for the Champions League. The result has done nothing either to boost his chances of keeping his job.
United dominated the final stages of the first half, but other than that they were matched or outplayed by Sunderland, who could have scored more.
Love appears on Valentine's weekend
Manchester United now have seven defenders injured after they lost Matteo Darmian to a shoulder injury during the first half.
On Saturday, the day before Valentine's Day, Van Gaal brought on the appropriately named Donald Love, a Scotland Under-21 international. The former Wigan loanee had a solid performance on his debut at right-back.
The 21-year-old joined in United's attack at will and showed he was not overawed when he screamed at captain Wayne Rooney for over-hitting the return ball of a one-two.
Man of the match - Wahbi Khazri
Wahbi Khazri had a key role in most of Sunderland's best attacks, with five key passes (all icons bar those in red are successful balls or a goal)
The 25-year-old was brilliant throughout, and caused United plenty of problems even outside of the two goals. On several occasions he dropped back and helped intercept attacks.
The stats you need to know
Sunderland recorded their first ever Premier League win against Manchester United at the Stadium of Light in their 14th attempt.
United have earned fewer points this season than in any other Premier League campaign after 26 games (41).
United have won none of the past seven league games where they conceded the first goal (D1 L6).
Sunderland attempted more shots (including blocks) versus United than in any other league game this season (21 shots).
The Red Devils have collected just six points from their past seven league away games (W1 D3 L3).
Only Wayne Rooney (18) has scored or assisted more goals in all competitions for United this season than Anthony Martial (15 - 10 goals, five assists).
Sunderland have gone 12 games without a clean sheet in the league, the longest current run in the division.
United have earned fewer points this season than in any other Premier League campaign after 26 games (41).
'We deserved to win'
Victory a big statement - Allardyce
Sunderland boss Sam Allardyce told BBC Match of the Day: "I thought the result was right. On the balance of chances created, a 2-1 win was no more than we deserved.
"It shows the importance of set plays. We've found a lad who delivers a great ball. One, he's scored himself and the second ball for Lamine's goal was quality.
"I thought Jermain Defoe was going to make it 2-0 and then Dame N'Doye got in one-on-one. We all prayed he would score. When he missed I wondered if it would be one of those days.
"Everyone is very happy at the moment. I've sensed a commitment and a desire and will to get out of the problems."
