Goals from midfielder Mark Noble and defender Matthew Upson in each half were enough for Gianfranco Zola's men.
West Ham had a chance to equalise when Kalou fouled Hireta Ilunga but Cech superbly saved Mark Noble's penalty.
James Morrison headed the Baggies in front before Mark Noble tapped in a rebound from David Di Michele's header.
But it was the introduction of Mark Noble, who came on for the ineffective McCarthy after 72 minutes, that really changed the game.
Ilan levelled from Carlton Cole's cross and Radoslav Kovac put West Ham ahead from the rebound after Chris Kirkland had parried Mark Noble's free-kick.
Mark Noble fired wide with an overhead kick and Gomes produced an outstanding one-handed save to palm Ba's venomous goalbound shot around the post.
He latched onto Mark Noble's through-ball and out-paced the Fulham defence before beating Schwarzer to the pass and poking home into the unguarded net.
The Hammers cranked up the pressure and Mark Noble was unlucky to see his clever one-two with Faubert fizzle out as he put his shot wide.
The landlord of a nearby pub, Mark Noble-Campbell, confirmed that Best had started to drink alcohol in his bar, but said he had never caused any trouble.
West Ham players, including Scott Parker, Carlton Cole and Mark Noble delivered the club's bid to run the stadium at 10 Downing Street at the end of September.
Mark Noble surged into the box, only to be denied by a brave tackle from Claude Davis, who was injured in the process and had to be replaced by Chris Morgan.
BBC: SPORT | Football | Premiership | Sheff Utd 3-0 West Ham
Mark Noble dallied on the ball in his penalty box allowing Heskey to win possession and when the ball was cleverly worked into the box via Luke Young, Bent glanced his header past Green.
The hosts flew out of the traps and with Scott Parker and Mark Noble working beautifully together in tandem in the centre of their midfield they began to exert serious pressure on Foster's goal.
But West Brom were rampant and their lead should have been stretched to three when Peter Odemwingie escaped the attention of Wayne Bridge from Mark Noble's corner, but could only find Green with his close-range header.
Meanwhile, West Ham players Carlton Cole, Mark Noble and Scott Parker were at Downing Street on Thursday to present the club's joint bid to run the 2012 Olympic Stadium, with the club and Newham Council having delivered their bid earlier in the day.
There was more goalmouth action to follow moments before the interval, Mark Noble coming close to putting the the home side ahead when he forced a great save from Camp, before the east Londoners finally took the lead again shortly after the restart.
Barrett's denial follows Wigan coach Brian Noble insisting the stories were wide of the mark.
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