Willian broke the deadlock in the 89th minute when his smart volley from outside the penalty area deflected off Steven Naismith and sneaked past Tim Howard.
The match-winning goal came moments after Gareth Barry was sent off for a second yellow card – but in the same melee, Branislav Ivanovic avoided any sanction for an apparent attempted headbutt on James McCarthy.
Chelsea were repeatedly denied by Howard on his first appearance since picking up a calf injury on Boxing Day, but looked to have taken the lead in the second half when Nemanja Matic fired into the net from the edge of the box.
The goal was disallowed, however, after the ball bounced off Ivanovic on its way past the Everton goalkeeper and the assistant referee flagged for offside.
Everton also had chances to take the lead after the break. Romelu Lukaku connected with Bryan Oviedo’s fizzing cross from close range but Petr Cech was quick to react, saving with his feet to keep the score level.
Chelsea could have opened the scoring in the first half. Matic and Willian fired early efforts over the bar from the edge of the penalty area, before Lukaku hit back for Everton with a low drive straight at Cech.
Chelsea continued to press before the break and Eden Hazard narrowly failed to connect with Cesar Azpilicueta’s floated cross.
The Belgian then hit a powerful strike that Howard gathered at the second attempt, with Lukaku following his compatriot’s lead and testing Cech again from distance.
Everton sent on Kevin Mirallas in the closing stages and the winger immediately fired over from distance.
It was Chelsea who eventually found the breakthrough, though, with Willian beating Howard at the death to maintain the hosts’ seven-point lead at the top of the table.
Chelsea: Cech (8), Ivanovic (7), Zouma (6), Terry (6), Azpilicueta (7), Ramires (7), Matic (8), Cuadrado (7), Willian (8), Hazard (8), Remy (7).
Used subs: Drogba (6), Fabregas (7), Cahill (5).
Everton: Howard (8), Coleman (7), Stones (7), Jagielka (6), Oviedo (6), Besic (7), Barry (5), Lennon (5), Naismith (6), Barkley (6), Lukaku (7).
Used subs: McCarthy (6), Mirallas (6), Gibson (6).
Man of the match: Tim Howard
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