Jose Mourinho's side looked set to see their advantage at the top of the Premier League shrink, but the midfielder's late goal sealed all three points in dramatic fashion
Jose Mourinho's side looked set to be frustrated by a stubborn Toffees outfit as the game entered the closing stages, with Nemanja Matic seeing a goal ruled out after his strike deflected off Branislav Ivanovic, who was stood in an offside position.
But the Brazilian's deflected effort in the closing stages beat Tim Howard to maintain Chelsea's advantage at the top of the table.
Earlier, Petr Cech who was preferred to Thibaut Courtois in goal, made an incredible reflex save to deny former Chelsea striker Romelu Lukaku from close range.
Gareth Barry was sent off for the visitors late on before Willian sealed a win with only stoppage time remaining.
Juan Cuadrado, making his first start for Chelsea, looked a threat and the big-money deadline-day recruit dragged a shot wide of the far post, before Tim Howard saved a Loic Remy header in a frantic start.
The lively Eden Hazard went agonisingly close to getting on the end of Cesar Azpilicueta's fine cross as Everton struggled to contain the leaders, but Chelsea were unable to find the back of the net before the break.
Everton manager Roberto Martinez replaced Muhamed Besic, who was shown an early yellow card, with James McCarthy at half-time and Chelsea were soon back on the front foot after the break.
Hazard was a constant menace to the Everton defence and the Belgium winger fired the ball across the face of the goal, but Bryan Oviedo was well positioned to avert the danger.
The outstanding Hazard then surged into the area, after producing some fine close control, before forcing a save from Howard. The Everton goalkeeper also had to be at his best to save Matic's well executed free-kick.
The busy Howard again demonstrated why Martinez was so eager to recall him when he produced a diving stop to keep out a measured Willian effort, before Cech showed his class at the other end to thwart an unmarked Lukaku.
Belgium striker Lukaku looked certain to convert Oviedo's ball in from the left, but Cech stood up to keep out his finish from only six yards out.
Mourinho replaced Cuadrado and Remy with Cesc Fabregas and Didier Drogba 20 minutes from time and Chelsea had a late goal disallowed when Matic's shot was deflected in off Ivanovic, who was offside.
Barry was then dismissed for a challenge on Willian which sparked a mass confrontation and there was more drama to come, as Howard fisted away a cross into Willian's path and he rifled home with the aid of a defletion to stun Everton.