Craig Dawson's header was not enough to stop Albion falling to a fourth consecutive league defeat.
The defender opened the scoring but was unable to prevent Kevin Nolan or James Tomkins scoring for the Hammers before half time.
Albion huffed and puffed after the break but were unable to find an equaliser.
Alan Irvine made two changes to the side which lost to Arsenal with Chris Baird and Victor Anichebe recalled; but who caught your eye? Joleon Lescott won the Arsenal accolade with 31% of the votes.
Click here to vote for your Albion man of the match.