Willian's 89th-minute goal has given Chelsea a hard-fought victory against Everton and keeps the West London club seven points clear of Manchester City.
Jose Mourinho's side began on the front foot as Nemanja Matic went on a rampaging run before his subsequent shot failed to trouble Tim Howard.
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However, the visitors nearly took an early lead themselves when Romelu Lukaku forced a save from Petr Cech, who was preferred to first-choice keeper Thibaut Courtois.
Chelsea continued to push for a breakthrough as Loic Remy turned Juan Cuadrado's cross inches wide of Everton's goal before bringing a save out of Howard.
Branislav Ivanovic squandered Chelsea's best chance before the break when he headed over the crossbar from only a few yards out, but Roberto Martinez's men managed to reach half time with their clean sheet intact.
Howard needed to be alert early in the second half as he kept out efforts from Eden Hazard, Matic and a curling strike from Willian, but the Toffees almost found a shock breakthrough when Lukaku was denied again by the feet of Cech, following a pinpoint ball from Bryan Oviedo.
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Everton showed more confidence in attack in the latter stages as Lukaku turned provider for Kevin Mirallas only for the Belgian winger to blaze his shot over.
Chelsea thought they had snatched victory when Matic's deflected shot found the back of the net, but his effort was ruled out after Ivanovic helped turn the ball home from an offside position.
However, they finally found a winning goal with a minute remaining as Willian fired a shot through a crowded penalty area, which Howard was unable to keep out.
Chris O'Keefe
