The best of the chances during the first half fell to Winston Reid, but he volleyed over the top from close range.
The tempo was raised slightly after the interval, but West Brom saw their scoreless run stretched to three games – with two efforts from James Morrison which cannoned back off the crossbar as close as they came to forcing a breakthrough.
Albion made a promising start but the first semblance of a chance fell to the visitors, with Mark Noble heading a deep cross from Carlton Cole over the bar.
West Brom striker Peter Odemwingie was on target with a low 25-yard drive, although Jussi Jaaskelainen got his body behind the ball.
But there was little goalmouth action in the opening quarter of the game as both sides struggled to find a creative spark, although Morrison ventured forward to fire a low shot past the post.
Chris Brunt drilled a long-range attempt into the hands of Jaaskelainen before Reid spurned a gilt-edged chance for West Ham.
Cole stung the palms of Albion keeper Boaz Myhill with a 30-yard drive but it was Albion who started the second period on the offensive and Morrison’s hooked volley struck the top of the bar.
Then the Scottish international sliced his shot wide after Gareth McAuley had headed a fourth successive corner from Brunt into his path.
Reid produced a vital clearance to turn a low Odemwingie centre over his own bar under pressure from Long. But West Ham looked dangerous on the counter-attack and Joey O’Brien volleyed over at full stretch from a deep Noble free-kick.
Morrison struck the bar for the second time with 17 minutes remaining with a header from Brunt’s corner.
Cole nearly made the breakthrough in the final seconds when his snap shot had Myhill scrambling across his line to save at the foot of a post but a draw was a fair outcome.