Thiago Silva opened the scoring for the Blues early on before Tammy Abraham netted twice in quick succession in the second half to end the tie with a big win.
Frank Lampard's side struggled to create chances in the match but pounced on some defensive errors by the Hammers to seal all three points.
The victory brings Chelsea up to fifth in the Premier League standings, just a point behind Everton. Meanwhile, West Ham United drop to 10th place in the points table.
Here are the hits and flops from the match:
Hit: Tammy Abraham (Chelsea)
After four goalless outings, Tammy Abraham was finally on target again, netting a quickfire brace in the second half to sink West Ham.
Both goals were simple finishes, but the England star showed some predatory instincts in the build-up, turning up at the right place at the right time.
This performance will do a world of good for the Chelsea striker, who hasn't been at his usual best this season, netting only thrice before this game.
Should he maintain this form going forward, Abraham can also reclaim his position in the Chelsea side, which had come under threat after the arrival of Timo Werner.
Flop: Timo Werner (Chelsea)
Timo Werner may have assisted Abraham's first goal, bringing his tally up to five, but this statistic doesn't mask how poor he was during the game.
The German cut a desolate figure on the left wing, struggling to get into the match and even missing a great chance in the first half, firing right at Lukasz Fabianski after being put through on goal by Christian Pulisic.
Even though his assist tally continues to rise, Werner is falling desperately short in his main job of scoring goals - he's now gone six top-flight games without one!
Frank Lampard might be content with the margin of the scoreline, but Werner's barren run shows he's got a big problem at hand.