The Chelsea fans booed their team off the pitch after the visitors first took the lead and then twice equalised. Chelsea's inability to defend set-pieces cost them dear again.
But it started of brightly for the home side, four minutes in and a quick Chelsea counter-attack saw Didier Drogba flash a low, left-footer across Tim Howard's goal.
Everton, however had the best chance in the opening exchanges when Jo arrowed towards Petr Cech's goal a fine left-foot drive, which had the Chelsea keeper needing to be at his best to get down low to parry the ball to safety on 11 minutes.
Chelsea conceded the lead 30 seconds later when Leighton Baines' right-sided free-kick was met by the head of Louis Saha. The ball then hit Cech's left upright and bounced in off the goalkeeper for an own goal.
The league leaders were level within eight minutes. Ricardo Carvalho fed the ball to Frank Lampard on the edge of the Everton area, Lampard touched a deft left foot pass to Drogba, who powered home an excellent side-footer past a prone Howard.
Nicolas Anelka, five minutes later, put the Londoners ahead. Everton's Saha twice failed to clear the ball out of their own area, before Branislav Ivanovic tucked the ball to Anelka in the six-yard box. The French striker sidefooted home coolly into Howard's top left-hand corner.
Five minutes into injury time, and this time John Terry and Carvalho failed to clear - substitute Yakubu, just on for Jo, tapped the ball past Cech from two yards out.
But the lead was restored on 58 minutes for the home side when again Drogba latched on to a perfect byline cross by Ivanovic to volley home a smart right-footer past Howard from eight yards out.
It was a goal Chelsea's early second-half pressure warranted, but another set-piece foul-up allowed Everton to equalise again on 63 minutes.
John Heitnga's left-sided free-kick saw Drogba reach the ball but his header whacked the ball off the back of the head of Saha and it looped into the back of Chelsea net.
Chelsea searched for the winner - a brilliant free-kick by Michael Ballack almost brought number four but Howard clutched the ball out of the air.
Carvalho had a fine chance from a Florent Malouda corner but headed over the bar.
A last-gasp effort by Ballack saw his shot flash the ball wide of goal as Everton soaked up the pressure and were delighted to hang on for a point.