It did not take long for the Hammers to take the lead in the clash of two mid-table clubs.
In the second minute, West Ham were awarded a controversial penalty as Norwich defender Ryan Bennett pulled on the shirt of the Hammers' Winston Reid.
The call by referee Mark Clattenburg did not please Norwich manager Chris Hughton, who was irate on the touchline after the whistle had been blown.
After the Norwich players were done debating the call with Clattenburg, Mark Noble slotted home the first goal of the match for the Hammers.
The Canaries came close to equalizing the match in the 21st minute when Robert Snodgrass' free kick hit the right post.
Just five minutes later, the Hammers delivered a knockout blow to their guests as Joey O'Brien knocked home his second goal of the season.
West Ham could have gone ahead by three or four in the first half, but they were unable to finish two great chances on goal.
The first missed chance for the Hammers came in the 24th minute when Norwich keeper Mark Bunn made a spectacular save on Jack Collison. Bunn was forced to dive to his left, and his outstretched arm made contact with the ball to deny Collison's shot on goal.
Carlton Cole also had a clear chance on goal in the 36th minute, but he skied his shot over the crossbar after a magnificent cross that was sent in by Guy Demel.
Norwich did not go down easily late in the match as Russell Martin scored a goal in the 90th minute off of an Elliott Bennett corner kick.
However, that would be all the Canaries could muster towards the end of the second half as they failed to score an equalizer.
Both clubs will now take the weekend off from EPL play as they enter the third round of the FA Cup.
Norwich will visit London Road to play Championship club Peterborough United on Saturday, while the Hammers play in the marquee match of the weekend at home against Manchester United.
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