Arjen Robben broke Everton's stubborn resistance as Chelsea's Premiership challenge gathered pace.
Robben raced on to Eidur Gudjohnsen's pass to beat Nigel Martyn for his first Premiership goal after 72 minutes.
Everton were cursing a glaring miss by Alan Stubbs, who headed Leon Osman's cross wide from only eight yards and Tim Cahill twice tested Petr Cech.
But Robben also brought a fine save from Martyn and Gudjohnsen wasted a glorious chance from only eight yards.
The early exchanges were lively, with opportunities at both ends as Everton demonstrated they were ready to match Chelsea.
Everton's Alessandro Pistone was fortunate to deflect Frank Lampard's shot wide after the Italian defender slipped.
And after 18 minutes it needed a brilliant save from Chelsea keeper Cech to stop Everton taking the lead.
Kevin Kilbane's cross was perfect, and Cech dived to his left to stop Cahill opening the scoring with a trademark header.
The rest of the opening period was a story of constant Chelsea pressure being met with resilient Everton defence.
Everton goalkeeper Martyn was in acrobatic form to turn Robben's 20-yard drive over the top, then it needed a desperate clearance from Hibbert to deny Gudjohnsen.
Martyn was also on hand to block Gudjohnsen from point-blank range as Chelsea pressed to break the deadlock.
It was a familiar pattern after the break, with Kilbane booked for hauling down Paulo Ferreira as Everton dug in again.
Everton captain Stubbs missed the best chance of the game after 57 minutes when Chelsea switched off at a corner.
Leon Osman's cross found Stubbs unmarked and the veteran defender somehow headed wide from only eight yards.
Robben was the game's outstanding figure, and he was again within inches of opening the scoring when he curled a 25-yard free-kick narrowly off target.
And as the pressure mounted, Gudjohnsen was guilty of an awful miss after 70 minutes, failing to hit the target from eight yards from John Terry's knockdown.
Inevitably, it was Robben who broke the deadlock two minutes later with a stunning goal.
Gudjohnsen sent the Dutch winger clear, and he showed burning pace before lifting a precise finish over Martyn.
Cahill was dangerous again as Everton responded instantly, forcing Cech into another fine save.
Chelsea: Cech, Paulo Ferreira, Ricardo Carvalho, Terry, Babayaro, Makelele, Lampard, Tiago (Kezman 58), Robben, Duff (Huth 82), Gudjohnsen (Geremi 78). Subs Not Used: Cole, Cudicini.
Goals: Robben 72.
Everton: Martyn, Hibbert, Weir, Stubbs, Pistone (McFadden 84), Watson (Campbell 80), Osman (Chadwick 90), Cahill, Gravesen, Kilbane, Bent. Subs Not Used: Turner, Yobo.
Booked: Kilbane, Gravesen, Bent.
Ref: M Riley (W Yorkshire).