Former Hammer Frank Lampard strode into the box to head home the first goal of the afternoon after only 19 minutes from a Eden Hazard cross.
The Hammers had only minimal opportunities in the first-half as Chelsea dominated both in terms of both possession and chances.
The second-half started much as the first half-finished and Chelsea were quickly two goals up from a fine strike by Eden Hazard after a one-two with Spaniard Juan Mata.
Chelsea then controlled the rest of the game to secure a valuable three points and in the process dumping the Hammers down to 14th in the Premier League table.