The hosts opened the scoring in the 24th minute when Hazard showed great skill to dance past three defenders at pace and send a low drive past Lukasz Fabianski.
Two minutes later Hazard teed up Gonzalo Higuain, only for the striker’s shot from a tight angle to ricochet off the post.
West Ham improved after the interval with Manuel Lanzini’s shot pushed away by Kepa Arrizabalaga and Aaron Cresswell’s drive drifting inches wide.
Marko Arnautovic’s header was also deflected wide by Emerson.
However, Hazard doubled Chelsea’s lead on 90 minutes with a clinical 16th goal of the season giving Chelsea a third successive victory to take them above Tottenham Hotspur and Arsenal on 66 points.
West Ham remain 11th with 42 points.
