Alvaro Morata scored on rebound after Ben Foster saved Eden Hazard's effort after 17 minutes.
Morata turned provider for Hazard with a flick down for the Belgian to round Foster and score six minutes later.
Marcos Alonso with superb finish from a tight angle after inch perfect free kick by Cesc Fabregas.
Hazard scored his second with a whipped shot to pile further pressure on Baggies manager Tony Pulis.
Salomon Rondon headed in Matt Phillips' cross after just five minutes but correctly ruled out for offside .
David Luiz unused on the bench for Chelsea having been dropped for the win over Manchester United.