⚽ From 3-0 down with 20 minutes left to 3-3 Arsenal mount stunning comeback.
Giroud headed the equaliser and was involved in each of Arsenal's three goals against Bournemouth
Arsenal completed a dramatic comeback at Bournemouth as they rescued a point in injury time having fallen 3-0 behind.
The Gunners looked destined for a third away league defeat in a row before a late rally that began with a diving Alexis Sanchez header and gathered momentum when a stunning Lucas Perez left-footed volley reduced the gap to a single goal.
Bournemouth went down to 10 men when Simon Francis was sent off for a challenge on Aaron Ramsey and Arsenal capitalised as Olivier Giroud headed a 92nd-minute equaliser.
The home side had overwhelmed the Gunners early on and taken the lead when Charlie Daniels cut inside Hector Bellerin and stroked a shot past on-rushing keeper Petr Cech.
Callum Wilson scored a penalty to extend Bournemouth's lead and Ryan Fraser sent a shot through Cech's legs for the Cherries' third before the hour mark.
But the hosts buckled under Arsenal's late pressure as Arsene Wenger's side moved eight points behind Premier League leaders Chelsea, who play Tottenham on Wednesday.
Arsenal had produced a feeble display for 70 minutes and were second best in the face of Bournemouth's energy and desire but that all changed when Sanchez headed in at the far post following Giroud's flick-on.
Sanchez has scored 10 goals and assisted three more in 10 Premier League away appearances this season
The momentum of the match changed and five minutes later Giroud clipped a lovely ball to substitute Perez and he sent an angled volley inside the far post.
Francis' sending-off helped Arsenal, although Cherries boss Eddie Howe felt it was a "harsh" decision by referee Michael Oliver.
Perez scores his first league goal for Arsenal
Giroud headed in from a Granit Xhaka cross as Bournemouth failed in their desperate attempts to hang on during six minutes of added time.
Simon Francis was last sent off in January 2015
Giroud has been involved in eight goals in his last four Premier League starts (six goals, two assists)
Mixed emotions for Arsenal
Arsenal have been accused of lacking the character to maintain a title challenge in recent seasons and they did little to change that perception before Sanchez's goal.
They were continually second best to the home side and frustrations rose to the surface in the first half.
Sanchez and Ramsey exchanged angry words at 2-0 down, while Giroud showed his annoyance when Shkodran Mustafi failed to find him with a pass that went harmlessly out of play.
That they regrouped in such thrilling manner was doubtless a relief but not one that entirely satisfied goalscorer Giroud.
"I'm pleased to help the team by scoring the equaliser but I'm still disappointed," said the Frenchman.
"It's nice to come back but the way we played at the end, that made me think we should have done better. At least we came back, showed great mental strength and I will take it."
Narrow miss for Bournemouth
On this date in 2009, boss Eddie Howe was taking caretaker charge of his first match at Bournemouth - who were then second from bottom in League Two.
Success with the Dorset side as they won promotion to League One saw Howe lured away by Burnley, before he returned in October 2012 to complete the club's transformation with two more promotions in three seasons.
It is a mark of the turnaround he has instigated that he and his side were left bitterly disappointed at failing to avenge their defeat at Emirates Stadium in November.
The Cherries' 3-1 defeat at Arsenal was harsh on them and they looked more than capable of making amends for the majority of this game as the Gunners struggled to deal with their attacking 4-4-2 formation.
Even with the Arsenal comeback under way, Howe's men had a chance to go 4-2 up when Dan Gosling turned superbly in the visitors' area only to shoot well wide of Cech's goal.
A point keeps the Cherries ninth in the table.
What they said:
Arsenal manager Arsene Wenger: "At the start we suffered from the quality of Bournemouth. One team had over three days to recover and on top of that we suffered at the back.
"It was a physical test but we came back into the game and we showed we are mentally strong. I am happy to play every day but only if our opponent has done the same."
Bournemouth boss Eddie Howe: "It's a strange one for us. At 3-0 up you hope the game is over but you can't underestimate the quality of Arsenal and as soon as they got the first goal the game changed.
"We didn't see the game out in an effective manner from our perspective but you have to praise their resilience."
What next?
It's FA Cup third-round action for both these teams in their next outings with Bournemouth at Millwall at 15:00 GMT on Saturday, 7 January and Arsenal at Preston for a 17:30 kick-off on the same day.
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Olivier Giroud scored his second goal in as many games
Olivier Giroud's incredible scorpion kick set Arsenal on the way to a victory over Crystal Palace which moved them up to third in the Premier League.
With a cross from Alexis Sanchez delivered behind him, Frenchman Giroud elastically reached the ball with his left foot, looping it over his head and in off the underside of the bar.
An Alex Iwobi header gave Arsenal a scrappy second before Palace briefly rallied to force saves from home goalkeeper Petr Cech.
The win moves the Gunners back to within nine points of leaders Chelsea, while Palace stay 17th, two points above the relegation zone.
The visitors have won only once in 13 league games, with manager Sam Allardyce awaiting his first victory since taking over from Alan Pardew.
Giroud's magnificent moment of magic
Giroud was about 12 yards from goal when he applied his sensational finish to Sanchez's cross
Match Highlights
Giroud marked his return to the Arsenal starting line-up on Boxing Day by scoring the only goal in the win over West Bromwich Albion, and followed up here by pulling off one of the most memorable moments of this or any other season.
If anything, Giroud's was even more impressive, an acrobatic finish to a head-high cross delivered from the left by Sanchez at the end of a pacy Arsenal counter-attack.
As the ball arrived, a sprinting Giroud turned to stick out his left foot, flicked the ball over his head and saw it arc over the leap of Palace goalkeeper Wayne Hennessey, off the woodwork and into the net.
"It was an unbelievable finish," said former Arsenal defender Martin Keown on BBC Radio 5 live. "It has to be up there with the goal of the season already.
"He's hooked that with a gadget foot - the ball is behind him and he has no right to get his foot to it."
'The best goal I've scored' - what they said
Olivier Giroud told BBC Sport: "It is not difficult to say it is the best one. I was a bit lucky but it was the only thing I could do, the ball was behind me and I tried to hit it with a backheel.
"Maybe Henrikh Mkhitaryan's goal inspired me, it's the only thing you can do in that position. It is nice for me and the team because we start the year with a win."
Crystal Palace goalkeeper Wayne Hennessey on Sky Sports: "It was a wonder goal - there seems to be a lot going in recently. It's a fantastic strike."
Arsenal manager Arsene Wenger: "It was a great counter-attack at great speed, his reflex surprised everybody who knows football and that's what makes the goal great.
"I have been a bit spoiled over the years by the exceptional quality of the players I've had, but it will be remembered as an exceptional goal.
"Olly is very good in front of goal, but I've never seen this kind of goal from him."
Man of the match - Olivier Giroud
Though Arsenal's full-backs were outstanding, it would be churlish not to single out Olivier Giroud, who produced something quite special.
What's next?
Both teams are in action on Tuesday. Arsenal make the trip to Bournemouth (19:45 GMT), while Palace host bottom club Swansea (20:00).
Giroud scored his fourth top flight goal of the season with his effort against West Brom
Arsenal striker Olivier Giroud struck a late winner as the Gunners ended a run of two Premier League defeats with victory over a stubborn West Brom to climb back to third.
Giroud was making his first league start of the season and looped in an 86th minute header from a Mesut Ozil cross for his goal.
Until that moment the Gunners had enjoyed nearly 80% possession, but had struggled to find a way past inspired Baggies keeper Ben Foster.
He pulled off a number of key stops, including a double save when he parried an Alex Iwobi shot and blocked the rebound at the feet of Alexis Sanchez.
The 33-year-old former England keeper also tipped over a fizzing shot from Sanchez before West Brom nearly snatched a goal, with Claudio Yacob skying his shot over the bar after Arsenal keeper Petr Cech dropped a corner.
But Giroud finally broke the deadlock to keep Arsenal nine points behind leaders Chelsea, who beat Bournemouth.
Arsenal had buckled in defeats by Everton and Manchester City in their previous two games and the focus was on how they would respond against one of the more resolute teams to beat in the top flight.
It seemed like they were still feeling the impact of those losses as they had just one shot on target in the first half, but they managed 10 after the break as they increased their intensity and urgency.
Sanchez was their main threat as the Chile forward tried to drag the Gunners single-handedly to three points but, like his team, he found himself being continually frustrated.
Sanchez seemed set to score when he evaded a number of defenders in a run across the six-yard box only to strike his shot against the post, before Arsenal's persistence was eventually rewarded through Giroud.
"It has been a big relief," said the France striker. "We pushed to the end, kept believing in our game.
"We were very strong altogether and showed a good strong mentality. It was very important to win. We have shown a big mental strength."
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.
Everton's Seamus Coleman scores the equaliser (Reuters)
Arsenal missed the chance to go top of the Premier League as Everton came from behind to secure a first victory since October.
The Gunners, who had won their previous three games, were rewarded for an impressive start as Alexis Sanchez's free-kick deflected in off Ashley Williams.
Everton equalised just before half-time when Seamus Coleman glanced home Leighton Baines' excellent cross.
The Toffees, encouraged by a vocal crowd, dominated thereafter and Williams powered home a late header to complete the turnaround.
Home captain Phil Jagielka was sent off in the dying minutes for a second bookable offence and Arsenal had two shots cleared off the line in a frantic finale.
But they could not prevent a first league defeat since their opening match of the season, leaving them three points behind leaders Chelsea, who have a game in hand.
Everton, meanwhile, are up to seventh, four points behind fifth-placed Tottenham.
Everton 2-1 Arsenal Highlights [ English Premier League 2016-17 Match ] 20′ 0 – 1 Alexis Sanchez scored in 20th minute with a lucky deflected freekick to put Arsenal in lead. 44′ 1 – 1 Seamus Coleman brought Everton back into the game at stroke of halftime. 86′ 2 – 1 Ashley Williams scored late in second half with a thumping header to make it 2-1 for Everton. WHAT THE MANAGERS SAY:
Everton manager Ronald Koeman on BT Sport:
"The first 20 minutes, that was really poor. We were very nervous and unsure. Every ball back. Mistakes and no aggression. After that we played face to face and showed unbelievable spirit to come back and we deserved the win. We were lucky in the last situation but we played great football and the support of the fans, it makes Goodison Park really difficult to beat us here.
"Sometimes it is difficult to understand why we start so poorly at the beginning. Of course there is some lack of confidence but show your personality. We showed big personality." "We showed two faces. The first face I hate that face because it is all about being nervous. You cannot lose the game like that. This was a good match though because we showed how we have to play - with commitment and aggression. You see the reaction of the crowd when you go for it and that's what we did.
"On Monday, the game against Liverpool is of course a totally different situation now we go with three points in the pocket. We know we are strong at home and still unbeaten. If we play with the passion we showed tonight we will do well. We will learn from this match, it was a great result."
Arsenal manager Arsene Wenger, speaking to BBC Sport:
"I don't think with five to go we deserved to lose the game but we were caught on two headers. I think especially on the first one we were guilty, the second one was from a corner. We controlled Romelu Lukaku well but two defenders scored. Maybe we made it easy for them when they became more physical. They played a real cup game tonight.
"They defended well even when we controlled the game. We created chances but not too many were clear-cut. We battled hard. We put everything in and the players are very disappointed."
"It was a very physical game, we faced many physical challenges and that disturbed our game but we were a bit unlucky to lose as well.
"We had chances in the first half, especially from Mesut. They defended well, they played a cup game, and at the end of the day it was two defenders in their team who scored.
"They were a bit scared at first but they got their confidence. We did fight, I cannot fault that."
What next?
The win could not have come at a better time for Everton as they prepare for Monday's Merseyside derby with Liverpool at Goodison Park (20:00 GMT). However, they will be without Jagielka following his dismissal.
Arsenal, meanwhile, are back in the north west of England as they visit Manchester City on Sunday (16:00 GMT).
Sanchez scored his hat-trick in 14 minutes and 29 seconds, and his third goal was perhaps the best of the lot
Alexis Sanchez's fine hat-trick secured an emphatic victory over West Ham at London Stadium as Arsenal moved up to second in the Premier League table.
Mesut Ozil opened the scoring with Arsenal's first shot on target after Angelo Ogbonna's mistake and Sanchez's cut-back set up a simple finish.
The Hammers threatened to equalise after the break before Sanchez turned, drove into the box and finished brilliantly past Darren Randolph.
The Chilean added a second eight minutes later with a low strike into the corner, before Andy Carroll came on for a first appearance since 18 August and stooped to nod in the rebound from a Dimitri Payet free-kick that hit the bar.
However, any faint hopes of a comeback were extinguished by Alex Oxlade-Chamberlain's excellent finish from range and Sanchez's masterful dinked chip over the keeper.
The heavy defeat leaves Slaven Bilic's side one point above the relegation zone after Sunderland beat Leicester 2-1 earlier on Saturday.
Arsenal trail leaders Chelsea by three points but will slip to third if Liverpool win at Bournemouth on Sunday.
Arsene Wenger's side are now unbeaten in 13 league games, and their last away defeat was in February.
Sanchez's brilliance the difference
There was a 10-minute second-half spell during which many Arsenal fans might have recognised the familiar beginnings of a slump to draw or defeat despite having dominated for much of the game.
But Sanchez provided the match's key moment when he killed Shkodran Mustafi's booming pass from deep, turned past Anthony Makuanu and found the far angle of the net with brilliant ease with just under 20 minutes to play.
Arsenal defender Laurent Koscielny had been forced to clear a Manuel Lanzini cross bound for Ashley Fletcher from right underneath his own crossbar, West Ham's record signing Andre Ayew had just come on, and Carroll - who scored a hat-trick against Arsenal in a 3-3 draw in April - was being readied for action.
However, it was Sanchez's force that proved the most compelling. Each of his three goals were superbly taken but it was the final, hat-trick goal that will live longest in the memory.
Played through by Oxlade-Chamberlain, he feigned a dummy shot to fool already defeated Hammers keeper Randolph before delicately lifting the ball into the net for what must be one of the goals of the season so far.
'A big humiliation'
West Ham were certainly not helped by losing James Collins to injury in the game's early stages, and his replacement Alvaro Arbeloa looked off the pace.
But regardless of ill fortune, the Hammers remain without a win in the league since their home victory over Sunderland on 22 October.
Manager Slaven Bilic said this result, coming after Wednesday's 4-1 defeat by Manchester United in the EFL Cup, was "a big humiliation", and the fact that his players faded after Sanchez increased Arsenal's lead will be another cause for concern.
A win for Hull in their match at Middlesbrough on Monday will send West Ham into the bottom three.
Man of the match - Alexis Sanchez (Arsenal)
Not exactly hard to choose, this one. Arsene Wenger made the point that Sanchez was late to enter the game but when he did, his contribution was exceptional
What they said
West Ham boss Slaven Bilic on BT Sport: "I am not looking for excuses. Yes, we had injuries and mistakes, but we were not good enough.
"It was a big humiliation. I feel sorry for the fans and the club. We played some good games in this season, and had some good moments today even at 0-0 and 1-0 down.
"But I have to be honest and say we don't have the intensity and from the dedication comes the quality. We don't have it the same as last season, even in training.
"We are in a serious situation before this game which we don't like. The players know that, but it's not only about knowing but sacrificing, and your dedication for the game."
Arsenal manager Arsene Wenger, speaking to BBC Sport: "We had a convincing performance and strong result.
"We created many chances and you could see West Ham are not a confident team at home. On top of that we had a strong performance.
"Alexis Sanchez - it took him a while mentally to get into the game, but he can always give you something special. He's a fighter and a classy player. You don't find many players like him. He can always surprise you. He also has great technique as well.
"I believe we are on a strong run and it's down to us to be mentally ready to maintain that run."
What's next?
West Ham travel to Liverpool for a 16:30 GMT kick-off in the Premier League on Sunday, 11 December.
Arsenal play away to Swiss club Basel in the Champions League on Tuesday, before welcoming Stoke in the Premier League at 15:00 next Saturday.
