West Ham made the early running, with Marlon Harewood and Bobby Zamora trying their luck, with only a Paul Ince volley at the other end that went well over - to the obvious relief of the fans - to show for the visitors.
It looked for a moment as if West Ham had taken the lead when Harewood outfought Jody Craddock before unselfishly squaring the ball Zamora.
His celebration after tapping the ball home was short-lived - the linesman flagged for offside.
West Ham were again unlucky when Michael Oakes brilliantly tipped over a Calum Davenport header from a Matt Etherington corner.
Seyi Olofinjana had an ambitious 40 yard shot saved while Kenny Miller was denied after a Hayden Mullins tackle fell into his path, and Steve Bywater pushed his drive onto the outside of the post for a corner.
Nigel Reo-Coker then missed his chance to celebrate the captaincy with a goal, when, at the end of a quick break that involved Etherington and Zamora, he stroked the ball wide of Oakes' right hand post.
The Hammers continued to press, with Harewood heading at Oakes and Davenport glancing an Etherington corner agonisingly over.
Alan Pardew made two changes at the start of the second half, bringing on Sergei Rebrov and Steve Lomas for Etherington and Chadwick.
Rebrov played on the left, Lomas went to centre midfield, and Reo-Coker switched to the right.
Ince, given his usual Upton Park reception, had a thumping shot saved and shortly afterwards needed treatment from the Wolves physio for a facial injury.
With West Ham being frustrated, Teddy Sheringham replaced Zamora.
Harewood then made a superb driving run past three players only to see his hard, low cross flash across the goal towards the Chicken Run.
Harewood headed a Rebrov corner wide before nearly pressurising Mark Clyde into conceding a spectacular own goal; his high back pass flashed just wide of the beaten Oakes - and the post.
A Shaun Newton free kick was tipped over the bar by Bywater before the breakthrough finally came.
Joleon Lescott failed to clear, Sheringham took it off him, and coolly slotted home a low drive.
Sheringham nearly added a second with a header from an exquisite Rebrov cross and, though Oakes appeared to get a finger tip to it, no corner was given.
Sheringham had been replaced by Bobby Zamora in the starting line-up, with Nigel Reo-Coker made captain for the first time.
TEAM: Bywater, Repka, Fletcher, Harewood, Etherington [Lomas], Mullins, Reo-Coker, Zamora [Sheringham], Davenport, Chadwick [Rebrov], Powell.
Subs unused: Walker, Melville.