Late goals from Gabriel Martinelli and Nicolas Pepe kept Arsenal's slim European hopes alive, beating Crystal Palace 3-1 in Roy Hodgson's final Selhurst Park game.
However, Arsenal can now only finish in the Europa Conference League, with a Europa League finish now out of their reach.
Hodgson was given a guard of honour by both sides ahead of kick-off, but the niceties ended there. The game was a feisty affair as Arsenal chased a much-needed win to give them a glimmer of hope for European football next season.
Both sides saw openings in the first half, although few ended up on target. In fact, Arsenal scored with their only shot on target as Pepe (35) superbly turned home Kieran Tierney's cross.
Arsenal looked content to ride out the second half but, after a few near misses, Christian Benteke finally headed home in the 62nd minute after another pinpoint free-kick from Andros Townsend.
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Arsenal created very little after the equaliser but, somehow, scrambled the ball home late on as Martinelli (90+1) steered Martin Odegaard's pass over the line. Pepe (90+5) then wrapped up a vital three points for Arsenal, who still face an uphill battle to secure a European place next season.
Arsenal are ninth on 58 points, one behind Tottenham in seventh with Everton sandwiched in the middle. If they fail to secure European football on the final day of the season, they would be without a European spot for the first time in 25 years.
For Hodgson, it was a disappointing end to an otherwise spirited performance as he bid farewell to the Selhurst Park crowd for the final time ahead of his departure at the end of the season. Crystal Palace remain in 13th.
How Arsenal secured a vital win
Both sides had openings in the first ten minutes. Vicente Guaita was forced into a stretching save as Calum Chambers' cross searched for Pierre-Emerick Aubameyang in the middle. Smith Rowe then attempted something similar, this time aiming for Bukayo Saka, but no one was able to turn it home. At the other end, Gary Cahill sent a header just wide of the post.
In the middle of the half at it was Crystal Palace who continued to threaten. James Tomkins nodded goalwards from a Townsend corner, but Bernd Leno was down to save. It was another Townsend set-piece that saw Benteke nod over on the 30-minute mark before Jeffrey Schlupp's fierce drive forced another fingertip save from Leno.
Arsenal took the lead soon after with some sensational play from Saka and Tierney down the left. It included a sublime backheel from Saka to send Tierney into space for a cross, which Pepe turned home wonderfully with his first touch.
Palace survived two first-half VAR checks for red cards too. The first came inside five minutes as Schlupp was checked after a challenge on Chambers, but came away with a booking. It was a similar story for Benteke towards the end of the half after catching Mohamed Elneny in the chin with his elbow, but after a brief melee, it was a yellow card apiece for the pair.
The opening 15 minutes of the second half was a mostly quiet affair as Arsenal looked to preserve their lead, but their defences were breached just after the hour. Townsend delivered another fine free-kick and Benteke peeled away before leaping a header past Leno. VAR checked it for a foul from the striker in the build-up, but the goal stood.
Both sides had half chances as the game continued, but a late one-two from Arsenal saw them depart with all three points. Odegaard's ball into the area was bundled over the line from close range by Martinelli, with VAR allowing the goal to stand after a brief check.
Pepe's second of the even sealing the victory. Pepe drove into the area, taking on all comers and riding a few challenges, but driving the ball into the far corner.
Man of the match - Nicolas Pepe
The Arsenal forward has not always shown his best, but he was key for his team when they need a creative spark. His first goal was well taken and once made a driving run at the Palace defence, it resulted in another good goal.
Both of his shots on target in the game resulted in goals and he was also involved in the most duels (14) of the Arsenal team.
Arsenal manager Mikel Arteta said of his player: "I'm very encouraged and positive to think that way for two reasons. One, because he's come a long way, in terms of consistency of what he's producing in games. Not only in the Premier League but what he's done in Europe this season.
"And the second one, because of his serious mindset. He wants to look at every action, he wants to look at every post-match reflection we do with him individually. He wants to work and he wants to be the best. And when that happens and he has the talent that he has, I think it's a really good mixture."
What the managers said
Crystal Palace manager Roy Hodgson: "I'm a bit drained I suppose, it's been such a fantastic couple of days. I've been really quite knocked over by all the kind words and everything that happened here tonight, and yet I've seen us lose a game in the last four or five minutes in which we were good value for at least a point.
"The football part of me still feels that, but I know that I should be seeing the bigger picture and celebrating the reception that I got - the guard of honour, I've never seen that happen before, the reception from the fans and what's more, the performance the players gave me, especially in the second half when we really took the game to Arsenal and it looked as though we were capable of scoring against them.
"I hope when the dust settles, I'll have a happier feeling about what happened here tonight, but one thing I certainly will never forget is the reception that I've been given or all the incredibly nice things that have been said about my career. I suppose that does count for more than 90 minutes at the end of the day.
"I thought Arsenal started well and we weren't getting as close to them or stopping them in the way we would like, but we certainly did in the second half. I thought we were in control for large periods of the game so that makes the actual defeat a tough pill to swallow.
"I've got no regrets at all for the performance and I'm full of praise for the players in light of what they've had to deal with over the last couple of days."
Arsenal manager Mikel Arteta: "It was a crucial moment because we wanted to go into the final day with every chance to be in Europe next season. In order to do that we knew we had to win today and wait for some results, and with the way the game was developing, we were running out of time and it looked difficult. But at the end we found a way to do it.
"You saw me on the touchline. I'm so happy. When you're able to win a game in the last minute, it's always really pleasing because it shows the team how much they want it and [how much they] believe up to the last whistle, so really good.
"We have to handle that situation [on Sunday]. If somebody were to say to us in November or December that we could be in the position that we're in to have the chance in the last game to qualify for Europe, we'd have said you're crazy, but we've done it. I think what ourselves and the number of points that we've managed to get in those months, we have earned the right to be in that position. Now it's time to deliver on the final day, but unfortunately, it's not in our hands."
Opta stats - Arsenal win four in a row
- Arsenal picked up their first Premier League victory against Crystal Palace since January 2018, having been winless in five against the Eagles prior to today.
- Crystal Palace have lost their final home game in a Premier League season for the very first time (P12 W8 D3 L1).
- Arsenal have won four consecutive Premier League games under Mikel Arteta for the very first time; indeed, the Gunners have also won four consecutive away matches in the competition for the first time since October 2016.
- Following his brace this evening, Nicolas Pepe has scored in back-to-back Premier League appearances for the first time in his Arsenal career.
What's next?
Crystal Palace's final Premier League game of the season - and Hodgson's last game in charge - will be a trip to Liverpool on Sunday. Arsenal host Brighton in their last shot at a potential European finish. All Premier League games on Sunday will kick-off at 4pm.