Manchester United's 2-0 victory over Portsmouth cemented their place at the top, leaving the Blues trailing by six points, with the Red Devils also having a game in hand.
It was the visitors Jo who was the first to test Petr Cech on three minutes but his glancing header from eight yards out from a Steven Pienaar left-wing cross was met expertly by the Chelsea keeper.
Didier Drogba put the frighteners on Joseph Yobo a minute later but the centre-half cleared the danger.
Michael Ballack forced a diving save from Tim Howard on eight minutes as both sides sensed the chance of an early goal.
Chelsea, in the form of Frank Lampard, produced a trademark 25-yarder following an excellent five-man set up, but the 18th minute arrow just cleared Howard's crossbar.
Pienaar helped himself to a smart right-footed curling effort four minutes later. Thankfully for the under-fire Cech, the ball flew wide.
The Czech goalkeeper needed to be back to his best on 34 minutes to smother Tim Cahill's turn and right-foot shot, after a quick counter-attack caught the home side napping.
Everton continued to have the clearer of the chances and five minutes before half-time Cech was back-pedalling like mad as a Leighton Baines shot was deflected and just missed dipping into the net.
Three minutes later and clear on goal Jo fluffed the chance of the match , completely mis-kicking his shot with only Cech to beat.
Alex forced Howard into snuffling out a header from a Lampard corner a minute in to the second half.
However, Everton then raced upfield, forced Chelsea back, giving Cahill the space to have an excellent chance with a diving header from eight yards out. Again, Cech was equal to the task.
On 60 minutes Chelsea boss Guus Hiddink had seen enough and replaced the ineffectual Nicolas Anelka and Michael Essien with Salomon Kalou and John Obi Mikel respectively.
Within a minute the crowd shouted for John Terry to shoot from 30 yards and he duly obliged forcing Howard into the save of the match, just stretching to deflect the piledriver from the left-hand corner of the net.
Chelsea, now desperate for a winner, replaced Florent Malouda with Franco Di Santo with 18 minutes remaining, before Kalou forced Howard into two excellent stops.
With Chelsea now leaving space at the back, unbelievably for the Everton faithful, Cahill somehow screwed a gilt-edged chance wide and into Cech's side-netting on 83 minutes, following a rare breakaway. Pienaar also let fly, but was also wide from 20 yards.
The Blues' last chance fell to Drogba deep into injury time, he smashed in a fierce right-footer that rattled Howard's crossbar and flew away to safety to ensure that the game ended goalless.