The injury-hit Hammers dominated at Upton Park but missed the attacking abilities of Dimitri Payet, Diafra Sakho, Manuel Lanzini and Victor Moses.Mauro Zarate's shot cannoned back off the post, while Stoke was also denied by the woodwork when Marko Arnautovic hit the crossbar midway through the second half.
The hosts wanted a penalty just before halftime when Ryan Shawcross gave the ball away to Mark Noble and then pulled the West Ham skipper back in the area.
Cheikhou Kouyate's header was cleared from underneath the bar by Glen Johnson in stoppage time.
West Ham is provisionally eighth.
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