Stoke seemed to get the better start, worrying the visitors with several early warning shots.
Clive Clarke hit a long-range volley over the bar after only seven minutes, but it was Gifton Noel-Williams who came closer when his eight-yard header was pushed over the bar by Stephen Bywater.
Clarke posed West Ham another problem on 13 minutes when after patient build-up play he found some space just outside the area and fired a shot that fell just short of Bywater's right-hand post.
The Hammers broke the pressure and capitalised on only a half chance in the 39th minute when Bobby Zamora scrapped to win the ball on the left side of the box, allowing David Connolly to take his chance and weakly roll the ball past the static Neil Cutler into his bottom left corner.
The away side doubled their lead in the 58th minute with Stoke simply unable to cope with West Ham's pacy attacks.
Matthew Etherington's cool chip over Cutler failed to reach the goal, but Marlon Harewood was on hand to tap the ball into an empty net from close range.
Tony Pulis changed to a 4-5-1 formation after the break did little to help the side with Noel-Williams looking decidedly sluggish.
Kris Commons proved Stoke's only threat when he volleyed into the sidenetting late on.