Fernando Torres scored his first league goal since December as Chelsea secured third place in the table and an automatic place in the Champions League group stages with a 2-1 home win over a fine Everton side at Stamford Bridge.
With London rivals Arsenal winning 1-0 at Newcastle, Chelsea needed a second goal to ease the tension around the ground and Torres provided it with a fine winning goal on 76 minutes as he volleyed into the net after substitute Victor Moses had provided him with a cushioned header from Oscar's cross.
In a breathless and brilliant contest that could have gone either way, Chelsea completed a rousing week after lifting the Europa League with their 2-1 win over Benfica on Wednesday.
Chelsea moved ahead on seven minutes when visiting goalkeeper Tim Howard failed to hold a Demba Ba effort as Juan Mata slotted the rebound with some ease.
Torres was booked for a late tackle on Seamus Coleman in the first half and was fortunate to avoid a red card after diving in the box under pressure from Marouane Fellaini.
The Spanish striker sarcastically applauded a linesman, a gesture missed by referee Anthony Taylor that would have surely saw him walk.
Everton always looked as dangerous as the hosts in their attacking forays and equalised when Steven Naismith lifted the ball over Petr Cech on 14 minutes to restore parity after Victor Anichebe had played provider with some lovely play as David Luiz was penalised for losing the ball with a heavy first touch.
It was David Moyes's last match as Everton manager before he departs to succeed Sir Alex Ferguson at Manchester United. His side finish the campaign in sixth spot, two points above Merseyside rivals Liverpool.
Rafael Benitez is also likely to be moving on from his successful seven-month spell at Chelsea with Jose Mourinho widely expected to return to the club from Real Madrid.
Benitez can depart with real satisfaction having led Chelsea to a trophy while they also avoid having to qualify for the Champions League, a scenario that fourth-placed Arsenal must now confront in the final play-off match for European football's elite competition.
Everton substitute Nikica Jelavic should have rescued a point for the visiting team late on, but he somehow ended the match without a goal.
He knocked Leighton Baines's ball wide on 74 minutes before driving a shot straight into the arms of Cech on 81 minutes.
Cech then clawed out the Croatian forward's header five minutes later after a wonderful cross from Baines as a tiring Chelsea clung on for the three points.
The first half was a joy to watch on a balmy day at Stamford Bridge as both teams set about their task with some relish.
Howard was guilty of spilling a Ba shot and Mata was gifted the rebound as he converted with some simplicity.
Naismith should have equalised on 10 minutes when he nudged Coleman's cutback wide from 12 yards out.
But the former Rangers man played a leading role in the equaliser as a heavy first touch by Luiz enabled Anichebe to earn possession.
He supplied Naismith, who coolly lifted the ball over Cech to end his sequence of 20 games without a goal.
Everton were suddenly warming to the task as Darron Gibson saw a shot come back off a post with Cech beaten.
The effort spun off the frame of the goal with Cech fortunate the ball did not come back off him and end up in the net.
Torres headed wide with Nathan Ake lifting a shot over from distance as the play continued to rage from end to end.
Kevin Mirallas then came up with a feeble finish for Everton when his attempted volley from Gibson's cross was easily held by Cech.
Howard redeemed himself in the Everton goal to beat out a powerful shot by Mata after bounding onto a pass from Frank Lampard, who was presented with an award before kick-off by Bobby Tambling who he overtook as the club's all-time top goalscorer last weekend.
Pienaar saw an effort come back off the frame of Luiz moments before half-time, but Everton needed some fine defending by Phil Jagielka to prevent Gary Cahill from scoring in the second half.
In the end, the huffing and puffing all came to nothing as Torres made his 22nd goal of the season in all competitions and an 80th Premier League of his career count towards those Champions League riches.
MAN OF THE MATCH
Juan Mata (Chelsea) - Was given a standing ovation after he was replaced by César Azpilicueta in the closing moments. A class apart with his control and vision.
Chelsea: Cech 7, Ivanovic 5, Cahill 7, Luiz 6, Cole 7, Ake 7, Lampard 7, Torres 8, Mata 9, Oscar 7; Ba 7..subs: Azpilicueta 6, Ferreira 6, Moses 7
Everton: Howard 7, Coleman 7, Baines 7, Jagielka 6, Distin 8, Gibson 7, Fellaini 6, Pienaar 6, Mirallas 6, Naismith 6, Anichebe 7..subs: Heitinga 6, Jelavic 6