The Hammers were looking for a response having been hammered 4-1 by London rivals Tottenham Hotspur last weekend, whilst West Brom were hoping to build on a 2-1 win over Arsenal - but neither side really got what they will have wanted.
West Ham took the lead in the first half as Argentine forward Mauro Zarate whipped a sensational free kick in to the top corner of the net, leaving Baggies goalkeeper Boaz Myhill with absolutely no chance.
Tony Pulis then brought Rickie Lambert on at half time in order to try and inject an attacking threat in to his West Brom side, and it was the ex-Liverpool man who had a big part in the equaliser.
After Darren Fletcher controlled the ball, Lambert smashed a shot towards goal, and it cannoned off Winston Reid's hand and in to the net, to the despair of West Ham stopper Adrian.
West Ham pushed and pushed for a winner, but they were almost caught out as Jose Salomon Rondon's close-range header was kept out by Adrian.
The Hammers did have one golden chance late on, as Manuel Lanzini's looping cross was met by Victor Moses, but the Nigerian international could only volley the ball wide of goal.
The result means that West Ham and manager Slaven Bilic are without a win in four games, whilst West Brom cement their place in mid-table.