Cahill had in a bid to intercept a Jesus Navas’s cross acrobatically volleyed into his own net on the stroke of half-time.
Chelsea came firing from all cylinders in the second half and were rewarded when Costa pulled them level after a brilliant pass from Cesc Fabregas, with the striker doing well to shrug off Nicolas Otamendi before scoring.
The Blues then struck twice on the counter-attack as Costa turned provider for Willian who finished instinctively with a low shot, before Hazard sealed three points that could prove in the title race late on.
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Meanwhile, Willian dedicated his goal to members of the Brazilian club side that lost their lives in a plane crash by removing the black armband he wore and raising it into the air