Fernando Torres scored his first Premier League goal of 2013 as Chelsea marked Rafael Benitez's last game as manager by securing third place and Champions League football for next season with a thrilling victory over Everton.
Torres steered home the winner with 14 minutes left of a breathless game to round off a memorable week for the Europa League winners.
Juan Mata slotted the hosts ahead but David Moyes, in his farewell match after 11 years as Everton boss, saw his side level through Steven Naismith.
The Gunners needed a win and for the Blues to lose to be certain of finishing third and avoid facing a two-legged play-off to reach the group stages.
And despite a great start, for a long time the hosts gave Arsenal strong hope of at least earning an unprecedented Premier League play-off as both sides could have finished level on points, goal difference and goals scored had Chelsea drawn.
A gloriously sunny day full of positivity was in stark contrast to the cold, miserable conditions and accompanying poisonous atmosphere that surrounded Stamford Bridge in November when Benitez replaced the popular Roberto Di Matteo.
But there was no sense of unrest early on here. The home side looked sharp and, having controlled possession and territory, went ahead after seven minutes.
Tim Howard spilled Demba Ba's shot after a flowing move involving Mata and Oscar, and the Spaniard followed up to slot the ball home with ease.
But the visitors, with Moyes looking to secure the highest points tally in his 11-year stint as Everton manager, responded in style.
Naismith guided a shot just off target, Darron Gibson shot over and Chelsea were on the back foot, suddenly looking jaded and disjointed.
Everton deservedly levelled when David Luiz - back in the defence with Nathan Ake making a classy Premier League debut in midfield - intercepted a pass but lost possession.
Naismith took full advantage of the Brazilian's absence to lift the ball coolly over the advancing Petr Cech.
It was nearly 2-1 moments later when a deflected Gibson shot hit the post, hit Cech on the head, hit the post again and rebounded to safety.
And the chances kept on coming in a breathless first period.
Torres headed wide, Ake shot over and Frank Lampard, presented with a golden boot before the game for becoming the club's record goalscorer, should have scored his 204th in a Chelsea shirt but shot wildly over.
Everton were playing with the greater cohesion and also creating good chances. Steven Pienaar was seeing plenty of the ball and finding space at will and went close with a rasping goalbound shot that was blocked by Luiz.
Chelsea upped the tempo after the interval with Oscar, playing an incredible 79th game of the season for club and country, their main threat.
Gary Cahill had a shot beaten away, Branislav Ivanovic - the midweek Europa League match-winner - horribly mis-kicked and Ba also had a curled effort deflected just wide off Sylvain Distin.
But Everton's defence, superbly organised by Phil Jagielka, was finally breached when Torres shot home from close range - his first Premier League goal in 1,179 minutes since he scored against Aston Villa in December.
And although Toffees sub Nikica Jelavic had a couple of chances to level, Chelsea were not to be denied and have now reached the group stages of Europe's premier club competition for 10 seasons in a row.
Everton manager David Moyes:
"Our players could have turned off and said that it didn't matter but we really gave Chelsea a good game. We played well, we were unlucky not to get more than nothing out of the game.
"It's been a great effort from the players. I've just said to them they've had a brilliant season. You can see the way they've played against the best in the country.
"Whoever takes the job will have a lot of pleasure working with them because they're honest, whole-hearted, have great energy and are a really good team as well.
"It's emotional because it's the last time I walk away from the players but part of the job is you move on. It's rare to stay in a job for 11 years so I'm thankful for getting that opportunity and hopeful they're in a strong position to push on."