Hazard, who has been strongly linked with a move to Real Madrid this summer, evaded five players during a stunning run, before the Belgium forward calmly beat keeper Lukasz Fabianski.
He added a late second goal to cap a magnificent individual performance in an entertaining game at Stamford Bridge.
Gonzalo Higuain hit a post, while Hazard was denied a penalty after what looked like a foul by Marko Arnautovic, with Argentine midfielder Manuel Lanzini going closest for West Ham with a shot which was beaten away by Kepa Arrizabalaga.
Chelsea, who can still qualify for next season’s Champions League by winning the Europa League, are three points ahead of fifth-placed Arsenal – who have a game in hand – after a third successive league win.
The Hammers remain 11th after a third defeat in four league games.
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