Cameroon full-back Geremi struck the only goal in a pulsating match which ebbed and flowed, and the East London side must rue their lack of punch up front.
Chelsea's first meaningful attack on three minutes was the result of a five-man passing move. Thankfully for the Hammers, the attack petered out.
A minute later, however, Chelsea skipper John Terry headed the ball over the Hammers crossbar, following a Frank Lampard corner.
Argentinian striker Carlos Tevez's shot was blocked by Ashley Cole and Lee Bowyer drove in from 20 yards. With Michael Ballack just one booking away from a suspension, which would mean him missing the away fixture against Manchester United next week, Jose Mourinho brought Arjen Robben back into the starting line-up.
On nine minutes, Chelsea keeper Carlo Cudicini was forced to make a fine diving save from a Paul Konchesky byline cross.
West Ham could have gone into the lead on 13 minutes. Unluckily for them, a well-worked corner saw full-back Jonathan Spector head the ball just over the Chelsea crossbar.
A minute later and Terry again headed just wide of goal from a Lampard corner, but Chelsea broke the deadlock and the decisive strike came on 22 minutes.
Didier Drogba was upended by Danny Gabbidon on the edge of the West Ham area. With Andriy Shevchenko and Lampard waiting, up stepped Geremi to blast home a vicious, curling right-footer past the despairing left-hand dive of Robert Green. It was only the 27-year-old's fourth goal for the Blues.
West Ham's Nigel Reo-Coker let fly from 30 yards on 35 minutes, but his right-footer was so wide, it almost went for a throw-in.
Chelsea should hit number two four minutes before half-time, but Robben found himself with the ball six yards out. But he somehow managed to slice his shot wide.
Seconds later and a West Ham counter-attack saw Reo-Coker shoot from six yards, only to see Cole block the certain goal.
Matthew Etherington had fine chance deep in injury time but his shot, from the edge of the penalty area, inched wide.
Lampard almost silenced the West Ham boo boys on 53 minutes, but his sliced right-footer from the edge of the penalty area, after good set-up play by Shevchenko, went over the bar.
A slip-up by Geremi let in Etherington on 61 minutes, but his byline cross was hacked away for a corner by Terry.
Bobby Zamora had his first effort for West Ham on 64 minutes after collecting the ball from substitute Khalid Boulahrouz's poor clearance, the striker attempted an audacious shot from 20 yards.
Sadly for him, the ball went embarrassingly high and wide of the Chelsea goal.
Ex-Hammers skipper Joe Cole entered the fray at the expense of the disappointing Shevchenko on 70 minutes.
West Ham Alan Pardew replaced ineffectual Zamora with Marlon Harewood a minute later.
Michael Essien skimmed West Ham's left upright on 72 minutes with a vicious right-footer from 25 yards.
Terry could have had a hat-trick of headers. The third, again from a Lampard corner, was rammed into the ground and bounced just over the crossbar.
Forty-year-old Terry Sheringham was brought on with ten minutes remaining to try and save the game for the Hammers.
But it was Chelsea who had the ball in the back of the net on 84 minutes, but Drogba, who slotted the ball home, was adjudged offside.
West Ham piled on the pressure, but lacked the ability to break down Chelsea's stout defence.