Chelsea, who have won their first five games of the season, were stunned when an unmarked Sol Bamba flicked home to put Cardiff ahead in the 16th minute, but Hazard replied twice before halftime as the home side upped the tempo.
He hit the bottom corner after dancing round two defenders to shoot low in the 37th minute, then latched on to another Olivier Giroud layoff with the Frenchman at full stretch in the 44th.
The Belgian scored a cool penalty in the 81st minute after Bamba brought down Willian in the area. Willian rounded off a satisfying afternoon for the London side, who moved top on goal difference, with a dipping shot from outside the area.
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