But if Arsenal still had hope then, it disappeared with Hazard’s wonder goal in the 53rd minute.
Gunners boss Arsene Wenger responded by sending on Olivier Giroud and Danny Welbeck, who was denied a headed goal by Courtois’ fine save.
But Arsenal were fortunate to finish the match with 11 men as Gabriel escaped unpunished when he smacked Hazard in the face.
And five minutes from time, Fabregas lobbed home and pointedly didn’t celebrate against his former club after ex-Chelsea keeper Petr Cech had made a hash of a clearance.
Chelsea, though, were denied their 14th clean sheet in the league this season, which would have given them the best defensive record in Europe’s top five leagues.
Arsenal finally scored in added time when Giroud headed home from Nacho Monreal’s cross, but it wasn’t enough for the Gunners. And too often in recent times that has been the case for Arsenal, who have now lost on their last five visits to Stamford Bridge.