Avram Grant's side is rooted to the bottom of the Premier League after going down 3-0 at Stamford Bridge.
Goals from Frank Lampard, Fernando Torres and Florent Malouda ensured West Ham remain bottom of the table, where they found themselves following the afternoon's earlier fixtures.However United can at least take heart from a spirited performance that belied the final score - a result that more than flattered the home side, who had to reply on two goals in the final five minutes to finally see off the Hammers.
After a slow start during which the home side created a number of half chances, West Ham began to find their feet and created three great chances to open the scoring within seven first half minutes.
Demba Ba forced Petr Cech to tip over a crashing drive on 24 minutes before Jonathan Spector - included at the expense of the injured Scott Parker - forced a similarly smart save from the 'keeper when his diving header from point-blank range was pushed round the post.
However United went closest to scoring ahead of the break on the half-hour mark when Freddie Sears' cheeky backheel beat Cech - but not full-back Ashley Cole, stationed on the goal line, who hacked Sears' effort clear.
Chelsea - who had begun stronger and created a number of half chances, the best of which came after just two minutes when Rob Green had to be at his best to smother a Malouda effort - were distinctly rocking at that point with discontent beginning to emanate from the stands.
However former Hammer Lampard silenced his team's impending critics with the half's only goal three minutes ahead of the breal. A Drogba ball down the line was sent back into the box by full-back Cole and converted by Lampard, arriving late - and unmarked - in the six yard box.
As per the first half, Chelsea began stronger after the break and Kalou had the first chance of the second half six minutes in when he screwed badly wide when well placed in front of goal.
But the Irons hit back with chances for Manuel Da Costa - who made a rapid recovery having appeared at court earlier this week with his leg in plaster - and Mark Noble; the former's effort being cleared off the line by Kalou.
Sadly for Noble, that aforementioned effort proved to be his final contribution of note as he left the field shortly after with what appeared to be a hamstring injury - yet another blow to manager Grant in a season littered with injuries. A few moments earlier Chelsea had lost the influential Michael Essien to a similar injury.
Lampard and Malouda then spurned chances to double their lead before Carlton Cole showed his bad side with a howler of a miss. However winner of 'biggest miss of the day' probably goes to Robbie Keane who, when played in by Spector with only Cech to beat on 73 minutes fired the wrong side of the post.
With Da Costa and Ba further testing Cech, hopes were high that United could grab what would have been a deserved point.
However two goals in the final few minutes sealed the win for the home side; the first coming from substitute Torres who took advantage of the conditions to score his first goal for Chelsea (after some 732 minutes) and the other in the third minute of injury time through Malouda, attoning for his miss approximately 90 minutes earlier.
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