A capital derby at the London Stadium produced a bright opening, with the hosts posing plenty of problems for the table-topping Blues.
It was, however, to be the kind of flowing counter that has become Chelsea’s trademark this season which allowed them to open the scoring.
Hazard exchanged passes with Pedro to spring in behind and the Belgian made no mistake as he calmly rounded Darren Randolph and rolled into the back of the net.
Costa then doubled that advantage five minutes into the second half as he bundled home his 17th league goal of the season from a corner.
Manuel Lanzini pulled one back in stoppage-time to set up a nervy finish for the visitors, but they were able to leave with all three points.