Tim Cahill's 90th-minute overhead kick denied Chelsea after Didier Drogba looked to have won the game for them.
Drogba made amends for a glaring miss by putting Chelsea ahead
Everton competed manfully early on and Steven Pienaar missed an opportunity when Leon Osman headed across goal.
But Tim Howard superbly kept out a Frank Lampard shot and Drogba wasted a glorious chance just before the break.
Alex had a shot cleared off the line by Tony Hibbert before Drogba headed in Salomon Kalou's corner, only for Cahill to stun the hosts in spectacular style.
It ended Chelsea's run of four straight Premier League wins but was no more than Everton deserved after a battling display.
They went into the game on the back of five victories in all competitions and were comfortable in the early stages, defending stoutly and maintaining decent possession, while trying to break in good numbers.
And so successful were they in their endeavours, they should have gone ahead in the 15th minute.
Pienaar found himself free in the six-yard box when Osman headed Yakubu's cross from the left flank back across goal, but the South African completely missed with his kick.
Chelsea gradually took charge, however, and should have been a goal up by the interval.
Their full-backs had been the likeliest source of opportunities and Howard magnificently palmed away a Lampard side-footed effort after Juliano Belletti had surged down the right and played the ball into him in the area.
Cahill's spectacular strike right at the end stunned the home side
Then Drogba, of all people, missed as easy a chance as he is likely to get at this level.
Left-back Wayne Bridge found Shaun Wright Phillips, who crossed to the big striker in acres of space with only Howard to beat, but the Ivorian somehow missed the ball completely.
Everton boss David Moyes had seen enough and replaced Phil Neville and Yakubu with strikers Victor Anichebe and James McFadden.
It was Chelsea who exerted pressure in the first 10 minutes of the second half, though, with Lampard at the heart of their attacking moves.
Everton were not content just to sit back and soak up the pressure - and in Anichebe they had a genuine physical presence at the other end.
Indeed, the home fans were starting to grow frustrated until Lampard's curling long-range effort was tipped over by Howard.
From the resulting corner, Howard punched the ball to Alex, whose shot was expertly cleared by Hibbert.
Having worked so hard to keep out Chelsea, the visitors will be disappointed by the ease with which Drogba escaped his marker at the near post to glance his header past Howard and Hibbert.
But Everton battled away right to the end and were rewarded when the impressive McFadden's shot was blocked and Cahill acrobatically pounced as Belletti hesitated.
Chelsea boss Avram Grant:
"It was one of our best games - we played very good football, created a lot of chances and from their one chance they scored.
"We moved the ball very well and played quickly. People like this but what happened is one of the reasons I don't because from nowhere they scored a goal.
"The most important thing is we created chances and didn't win the game but if we continue to play like this we will be going in the right direction."
Everton boss David Moyes:
"In the first half they had one or two chances and we missed a good one too. We had to change it to get a better grip of the game and I felt we did that.
"We were never out of the game, we were gritty and determined. We always felt if we could hang in there we had people on the pitch who can score goals and that's what Cahill does for us.
"McFadden's been unfortunate not to be involved. He made a difference in the second half with Anichebe. We had to change it, we were brave and got our rewards for it."
Chelsea: Cudicini, Belletti, Alex, Carvalho (Ben-Haim 29), Bridge, Essien, Wright-Phillips (Kalou 64), Obi, Lampard, Joe Cole, Drogba.
Subs Not Used: Hilario, Shevchenko, Pizarro.
Booked: Belletti, Essien.
Goals: Drogba 70.
Everton: Howard, Hibbert, Yobo, Lescott, Nuno Valente, Pienaar, Carsley (Gravesen 76), Neville (McFadden 46), Osman, Cahill, Yakubu (Anichebe 46).
Subs Not Used: Wessels, Jagielka.
Booked: Neville, Pienaar.
Goals: Cahill 90.
Ref: Alan Wiley (Staffordshire).