- West Ham United 1-3 Chelsea: As it happened
West Ham midfielder Scott Parker became the first player to score against the Blues this season but his late effort was scant consolation for the home side.
Chelsea's victory over their London rivals piled more pressure on under-fire manager Avram Grant, whose side remained rooted to the foot of the table without a single point from their opening four games and having conceded 12 goals.
In contrast, Carlo Ancelotti's team have now scored 17 and conceded just once, and their domination of this game began as early as the second minute when debutant Ramires won a corner on the left flank.
Essien rose above two defenders to head home Didier Drogba's cross to silence the home fans.
West Ham almost equalised moments later when new signing Victor Obinna sent a close-range effort straight at Chelsea goalkeeper Petr Cech.
The visitors went 2-0 up in the 17th minute, though, when West Ham's England goalkeeper Robert Green spilled a 30-yard Drogba free-kick.
Defender Matthew Upson tried to clear the loose ball but it cannoned back off Chelsea's Ivory Coast striker Kalou and over the head of the stricken Green.
Kalou went close to grabbing his second in the 21st minute but his shot was deflected around the post, much to the relief of the grounded Green.
Another corner from Drogba caused panic in the home defence but this time John Terry's effort was collected easily by Green.
West Ham should have pulled one back in the 27th minute but the unmarked Obinna put his volley wide from eight yards.
The Hammers striker then sent a curling shot just wide of the target after cutting in from the left wing.
Chelsea almost extended their lead when another Drogba corner fell to Nigerian midfielder John Obi Mikel.
His rising drive from 20-yards slammed against the angle of Green's left upright and the crossbar.
Chelsea received a scare in the 35th minute when Terry went down under a challenge from Carlton Cole, but the England defender continued after lengthy treatment - much to the disappointment of the home fans.
Ashley Cole became the first name in Chris Foy's notebook in the 40th minute when he was shown the yellow card for a foul on Herita Ilunga.
In the 43rd minute, Cech had to punch away a cross-shot from Ilunga as West Ham looked in vain for a way back into the game.
They almost succeeded in stoppage time but Carlton Cole's effort was ruled offside.
Ramires should have troubled Green in the 50th minute but fired over from the edge of the penalty area as Chelsea continued to dominate proceedings.
West Ham tried hard to lift the tempo of the game and substitute Kieron Dyer, on at half-time for Luis Boa Morte, almost broke through with a clever run into the six-yard box.
Chelsea almost made it three on the hour when Kalou collected a fine pass from Drogba only to send his curling shot inches wide of Green's right-hand post.
The visitors had clearly settled for the three points as their was little urgency in their play.
When they did show some ambition, Drogba forced Green into a fine save with a 20-yard shot.
Branislav Ivanovic was booked in the 64th minute for bringing down Carlton Cole.
A cross from Obinna three minutes later then found only the hands of Cech, much to the growing frustration of the home fans.
Mark Noble then sent a long-range effort just wide of Cech's right-hand post but the home side still lacked the killer touch.
Chelsea made it 3-0 in the 83rd minute when Essien headed home Paulo Ferreira's cross but moments later they conceded their first goal of the season when Parker calmly lobbed Cech from 20 yards.
West Ham substitute Frederic Piquionne wasted a great chance to reduce the arrears still further when he headed against the bar from just two yards.