The Hammers completely dominated the game in the first half and took the lead on 32 minutes when Ravel Morrison converted a pull-back from Captain Kevin Nolan after some fine work down the flank by Razvan Rat.
In the second half the Canaries were gifted an equaliser from the spot when Jussi Jaaskelainen brought down Gary Hooper. Robert Snodgrass then hit their second with a curling free-kick before Leroy Fer sealed all three points for Norwich with a goal in stoppage time.