Didier Drogba's brilliant long-range volley clinched the points for Chelsea after a thriller at Goodison Park.
Drogba celebrates his dramatic late winner for Chelsea
Mikel Arteta's first-half penalty put Everton ahead after John Terry's stand-in Khalid Boulahrouz hauled down the ever-threatening Victor Anichebe.
Chelsea levelled when Michael Ballack's free-kick hit the post and deflected in off the back of the diving Tim Howard.
Joseph Yobo headed Everton in front before Frank Lampard's looping equaliser and Drogba's late winner.
Chelsea started without captain Terry, who suffered a recurrence of a back problem that kept him out of the recent win at Fulham.
Everton posed the first serious threat, when Ashley Cole was forced to head Arteta's left-wing cross clear when under pressure from Leon Osman.
The main early talking point was a rejected penalty claim when Andy Johnson was caught between Boulahrouz and goalkeeper Hilario.
Referee Mark Halsey checked with the linesman before waving away any appeals, a decision that raised passions in both managerial dug-outs.
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Lampard saw a trademark long-range effort whistle just wide of the post and down the other end a shot on the turn from Arteta dribbled wide as Everton took the game to the champions.
The Johnson incident exposed Boulahrouz's discomfort, so it was no surprise when he was involved in Everton's first goal.
Anichebe, making his first Premiership start, was a constant threat and when he was wrestled to the ground by the Dutchman, Arteta netted from the spot.
Osman's injury-time header nearly doubled the lead but minutes after the restart the lead was gone, when Ballack's free-kick after Lee Carsley's needless handball went in off Howard's back.
Salomon Kalou then saw a close-range effort hit the post as a revitalised Chelsea started to take control of the game.
But then Yobo took centre stage, heading his first goal in 13 months to restore the advantage before racing back in defence to deny Drogba after a superb long ball by Lampard.
Just as Everton were starting to think of a famous win, Chelsea produced a dazzling late double-blow.
First, Lampard was left unmarked and thrashed the ball into the roof of the net from the right-hand corner of the box.
And then minutes after hitting the post, Drogba chested down a flick-on, turned and volleyed a stunning long-range winner.
Everton manager David Moyes:
"I can't be critical of my team in any of their performances except for the way they conceded the goals.
"When we got to 2-1, we knew they'd change their system, chase the game and push people forward and I thought we'd coped with that and seen it off - but for Lampard's goal.
"You can tell everyone what he's capable of but I thought we should have got to the ball quicker when it was rolled back to him, so for me that was disappointing."
Chelsea manager Jose Mourinho on coming for behind:
"Players with normal personalities would put their arms down and the game is lost.
"But they kept believing until the last second and fought for the result.
"I told them it's about belief. If you don't believe you have no chance.
"At this moment, everything looks like it's against us so they need to be very strong - and that belief they had was very important."
Everton: Howard, Neville, Yobo, Stubbs, Lescott, Osman, Carsley (Beattie 90), Davies, Arteta, Johnson, Anichebe (McFadden 90).
Subs Not Used: Wright, Naysmith, Weir.
Goals: Arteta 38 pen, Yobo 64.
Chelsea: Hilario, Geremi (Kalou 46), Boulahrouz (Bridge 73), Carvalho, Ashley Cole, Essien, Makelele, Ballack, Lampard, Drogba, Robben (Shevchenko 73).
Subs Not Used: Hedman, Ferreira.
Goals: Howard 49 og, Lampard 81, Drogba 87.
Ref: M Halsey (Lancashire).