Steven Pienaar had given the Toffees an early lead, after just a minute, stealing a march on his markers and pouncing when Victor Anichebe hit the post.
Chelsea withstood some early pressure but began expressing themselves after 30 minutes and drew level through a Frank Lampard header moments before half-time.
The second period was a typical pulsating Premier League tussle, in which Everton bossed the territory while Chelsea carved out the better chances via several speedy breaks.
The visitors eventually grabbed the points on 72 minutes, with Lampard once again on hand to stab home and make it 2-1.
Here's a look at the contributions of both sets of players.
Tim Howard: 6.5/10
Howard made a couple of smart saves and was blameless for the first goal, although he may perhaps feel unlucky to have diverted the ball towards Lampard for Chelsea's winner.
Phil Jagielka: 6.5/10
Needed at right-back due to his side's growing injury list, Jagielka gave a committed performance, but was understandably caught out positionally on a few occasions.
He was involved in the build up to Everton's goal and bailed out his side with a team-high eight clearances.
Leighton Baines: 7/10
Constantly involved going forward, Baines created two chances and sent in 13 generally dangerous crosses.
Arguably shadowed more than he has been all season by Ramires, the England man still produced going forward and didn't give away anything at the back.
John Heitinga: 7/10
A solid showing from the enigmatic Dutchman. Heitinga made a couple of timely interceptions, was accurate throughout with his longer passing, yet still appeared short of his very best form.
Sylvain Distin: 8/10
Everton's best player. The Frenchman used the correct blend of power and speed to nullify the threat of Fernando Torres and cancel out several Chelsea breaks.
Eight clearances, a pair of blocks and a high percentage of challenge success, Distin played one of his best games in an Everton shirt.
Thomas Hitzlsperger: 5/10
The left-footed Hitzlsperger looked slightly awkward in a more right-sided central berth, and struggled to impose himself on the game.
Shunted over to keep Baines, Pienaar and Osman playing in similar zones, the pace of the match seemed too quick for the German, who passed with only 66 percent accuracy.
Leon Osman: 7.5/10
With 85 touches, Osman was more involved than anyone else and passed at an impressive 92 percent accuracy, better than any other player.
Without the ball, he lost his man or was beaten a little too frequently, but still chipped in with more interceptions (five) than any other player.
Steven Pienaar: 7.5/10
Another prominent performer going forward, Pienaar drifted between areas on the left and behind Nikica Jelavić, and looked Everton's most likely threat going forward.
He took his goal well, created another chance, but should be passing better than 60 percent accuracy in the opposing half.
Steven Naismith: 6/10
With the game almost entirely focused on Everton's left, Naismith was often a peripheral figure. He was tidy enough on the ball and tracked Ashley Cole diligently before being replaced after 77 minutes.
Who was Everton's best performer?
Victor Anichebe: 7/10
Anichebe gets an extra point for his sheer commitment. The Nigerian left his mark on the Chelsea defenders, never stopped running and created two chances with some physical contributions.
Spent time as a striker and on the left flank and has performed admirably over the past three games in Marouane Fellaini's absence.
Nikica Jelavić : 6.5/10
On another day, the Croatian would have walked away with a brace and three points, but his two skillful efforts cruelly came back off the woodwork.
A better all-round performance, Jelavić linked up play and kept the ball better, although he was still caught offside a frustrating four times.
Apostolos Vellios: 6.5/10
The Greek under-21 international moved well and was physical in and around the penalty area. A player perhaps pushing for a larger role in the coming weeks.
Ross Barkley: 5/10
The much-hyped youngster showed why he needs another loan move to further hone his craft. Was dispossessed on a couple of occasions and looked a little rushed on the ball.
Bryan Oviedo: 6/10
Linked up on the left for a couple of intricate late moves, but his natural urge to hug the touchline clogged up space for an overlapping Baines.
Petr Čech: 7/10
Looked very assured in the first half, relieving his defence by diverting several dangerous crosses. Brought off at half-time with an injury.
César Azpilicueta: 6.5/10
Despite being kept very busy by Pienaar, Anichebe and a marauding Baines, the Spaniard was rarely beaten and stuck to his task well.
Targeted in the air against Anichebe, where he struggled, he made four interceptions and only David Luiz was on the ball more for Chelsea.
Ashley Cole: 6/10
Quiet game from Cole who did not have as much traffic coming his way. Rarely ventured forward and cut a strangely lethargic figure for Everton's goal, as he strolled after a clean-through Jagielka.
Gary Cahill: 7.5/10
Cahill was his side's best defender and was especially effective at set-pieces, taking authority and clearing the danger on a number of occasions.
Overall he made an impressive 13 clearances, passed well and was the game's most effective player in the challenge area.
Branislav Ivanović : 7/10
Coped well with the differing threats posed by Everton's strikers. His positional sense outfoxed Jelavic a number of times and he registered ten clearances, as well.
Also dealt well with a number of set-pieces and was a calming presence for his side during some frantic early scenes.
David Luiz: 7/10
Another accomplished midfield showing from Luiz, who was more involved than any other Chelsea player, and scurried after Everton's attackers throughout the game.
He enjoyed a testing battle with Pienaar, completed four interceptions and created a couple of chances in the final third.
Frank Lampard: 8.5/10
Everton fans will be sick of the sight of Lampard, who registered his eighth and ninth strikes in seven seasons against the Toffees, which once again proved decisive.
Aside from his goals, he was also the game's most creative player and is surely an attribute Chelsea would be wise to keep hold of this summer.
All-action display from the energetic Brazilian. Ramires was a constant threat going forward where he gave Everton several problems with some direct running and was involved in most of his side's attacks.
He contributed an assist and covered more ground than anyone else as he worked hard to keep up with Baines.
Juan Mata: 7.5/10
Showed several sublime touches and orchestrated a number of attacks, yet never quite opened up the defence as well as he can.
Still created two chances, passed well in the final third and found himself a lot of time and space in front of Everton's back four.
Who was Chelsea's best performer?
Eden Hazard: 6/10
As with every player on his side of the pitch, Hazard struggled to make an impact. He had almost half as many touches as his fellow midfielders but still made a smart contribution in the build up to the winning goal.
Fernando Torres: 6/10
Torres endured a frustrating afternoon as just one of his five shots tested Tim Howard.
He struggled to get away from the physical attentions of Distin, strayed offside four times and passed at just 61 percent accuracy.
Ross Turnbull: 6.5/10
The former Middlesbrough man was reliable enough in the second half, without being overly tested.
Victor Moses: 6.5/10
Moses offered a more direct threat to Hazard in the closing stages, which benefited Chelsea on the counter-attack.
Limited time to make an impact, but still able to launch a couple of important breaks to eat up the clock.