The East London side enjoyed near total domination over the Canaries after taking the lead through an early penalty, but the visitors got back into the game in injury time.
The Hammers got off to a flying start, winning a penalty that was expertly taken in the opening three minutes by Mark Noble.
The captain had a hand in West Ham’s second goal, as his pass was diverted into the path of Joey O’Brien, who caressed the ball into the bottom corner. Russell Martin added a late consolation strike for the visitors to put the result in question momentarily.
West Ham made the perfect start to the match, with referee Mark Clattenburg pointing to the penalty spot after Ryan Bennett had tugged on the shirt of Winston Reid.
The decision looked a soft one, the kind of incident that usually goes unpunished, and was greeted by cheers of happy disbelief from the home crowd and derision from the Canaries’ players. Noble stepped up to take the spot kick, sending Mark Bunn the wrong way.
Norwich struggled to mount a response until Robert Snodgrass’ 25-yard free-kick rattled the foot of the post, with Jussi Jaaskelainen rooted to the spot. Anthony Pilkington drove the ball inches wide of the post from the resulting corner.
Snodgrass’ effort seemed to wake the Hammers from the degree of complacency that had accompanied their early lead. Demel charged out of defence and crossed for Jack Collison, who forced a brilliant save from Bunn.
But it was only a brief respite for the Canaries, as left back O’Brien embarked on a run of his own, surging into the box before offloading to Noble. The captain’s pull-back deflected back into the path of the Irishman, who calmly slotted the ball past Bunn at his near post.
The Hammers should have extended their lead further just before the break when Guy Demel found Carlton Cole unmarked one-yard out from goal, but the forward somehow managed to blast the ball over the bar.
Norwich made a better start the second half, with Wes Hoolahan more involved. His through-ball put Harry Kane in, before the youngster buckled under the challenge of James Tomkins inside the box, but the visiting side’s pleas for a penalty were ignored by Clattenburg.
West Ham spurned more chances to extend their lead through Ricardo Vaz Te, who headed against the post after outjumping Martin.
The Scottish right-back managed a late consolation for the Canaries though. After good work down the right flank from substitute Elliot Bennett, Martin volleyed the ball into the back of the net -- his third goal in as many days -- but it was not enough for Norwich to steal a point.