Seeking to avoid a third successive Premier League defeat, Chelsea survived a nervy start when Salomon Rondon headed wide and Jay Rodriguez missed a glorious chance.
Ben Foster saved brilliantly from Davide Zappacosta and Olivier Giroud before Hazard struck on 25 minutes, with a turn, dribble and one-two with the Frenchman.
At the other end, Thibaut Courtois thwarted Rondon and Jonny Evans headed the ensuing corner over.
Chelsea took control when Victor Moses started and finished a move with Cesc Fabregas on 63 minutes.
Hazard crowned a fine display by scoring his 11th PL goal of the campaign.
Chelsea move a point above Tottenham Hotspur into fourth. West Brom remain bottom, seven points from safety.
Chelsea: 25 Feb v Man Utd (A)
West Brom: 24 Feb v Huddersfield Town (H)