Hayden Mullins gave a visitors an early lead and Bobby Zamora added a second early in the second half.
The Canaries pulled a goal back when Paul McVeigh beat Shaka Hislop from the penalty spot after James Collins at handle.
For home side kicked off attacking the barclay end goal, but found themselves a goal down inside a six minute when Bobby Zamora laid the ball back to Mullins whose fierce shot from the edge of the area found the net by the inside Robert Green's right hand post.
Their was a chance for Norwich after half an hour when Hislop failed to hold Adam Drury's cross but Dickson Etuhu fired over when the ball dropped at his feet.
Simon Charlton failed to find the target with a 25 yard free kick as the hammers looked content to go in at the break with a one nil lead.
Bobby Zamora and Marlon Harewood went close in the opening minutes of the second half and Harewood grazed the outside of Green's right hand post when he got a foot to Bobby Zamora's right wing cross.
Norwich then survived a free kick on the edge of the penalty area which set up Paul Konchesky for a shot that was deflected for a corner.
However, when Green failed to hold Matthew Etherington's cross come shot, Bobby Zamora
reacted quickly to head pass the prostrate keeper from a yard keeper.
Ian Henderson's shot was tipped over the bar by Hislop then Green did well at the other end to cut out another Etherington cross.
Mullins made well for Carl Fletcher at 67th minutes.
Three minutes later Norwich pulled a goal back. Collins used his hand to deny Peter Thorne a heading chance and Mike Riley had no hesitation in pointing to the penalty spot from which Paul McVeigh sent his lot the wrong way with a right foot shot to the keepers right.
Yaniv Katan made his debut when he replaced Bobby Zamora after 80th minutes.
Green had to be stretched off after a collision with Harewood as he pushed away. Paul Konchesky left wing cross and Darren Ward replaced him in the dying minutes.
Norwich - Gary Doherty. Didn't look out of place against an in-form Premiership strikeforce with an assured display at the back.
West Ham - Bobby Zamora. Set up the first goal and scored the second in an impressive display by the big striker.