Steve Clarke's side was twice denied by the crossbar as the Baggies failed to leapfrog Everton and move back in to the top five making it over five hours without a goal.
Scotland international James Morrison came closest for the home side as he was twice denied by the crossbar after an acrobatic scissor kick and a thumping header struck the framework as Sam Allardyce's side escaped back to the Boleyn Ground with a hard-fought point.
Both sides went into the game at The Hawthorns desperate to arrest their respective slumps, one which has seen the Baggies lose their last three games, while Allardyce's side has mustered just one win in its previous five outings.
The home side was without both Steven Reid and Liam Ridgewell through injury, meaning Billy Jones and Goran Popov deputized at their expense. The Hammers, meanwhile, were only able to name six substitutes in the Black Country and made just the solitary change, with Gary O'Neil replacing talisman Mohamed Diame after he picked up a hamstring injury in the defeat to Liverpool last week.
Both sides showed brief attacking glimpses in the opening five minutes but Matt Taylor's looping header failed to trouble Boaz Myhill. It took until the 15th minute for the first meaningful shot on goal though when Peter Odemwingie found space to turn and plunder a long-range drive comfortably into the arms of Jussi Jaaskelainen.
Morrison was the next to unleash an effort from distance, but he dragged his effort harmlessly wide before Shane Long turned on the edge of the area and skewed his shot the wrong side of the upright with his weaker foot. On the half-hour, Chris Brunt tested the Icelandic goalkeeper's reflexes with another piledriver, but the former Bolton stopper comfortably gathered.
Allardyce's side had barely ventured out of its own half in the opening 30 minutes, but Winston Reid should have put the visiting team in front when he somehow contrived to volley over James Collins' header back across goal from inside the six-yard box. It seemed to galvanize the Irons, and Carlton Cole was the next to pull the trigger when he stung Myhill's frosty palms but as halftime approached, neither side had demonstrated enough quality in the final third to break the deadlock.
The game finally sprung to life immediately after the restart and Steve Clarke's side was unlucky not to open the scoring after it put the visiting team under a barrage of pressure. A flurry of corners resulted in Morrison's speculative effort caressing the top of the crossbar.
West Ham responded through an unlikely source though, as Gary O'Neil cantered forward only to see his sumptuous curling effort drift narrowly the wrong side of the post before skipper Kevin Nolan slashed wide on the turn and the onrushing Matt Taylor fired an attempt off target following a neat move.
The hour mark passed without a clear cut opening and Zoltan Gera's fizzing drive was well beaten away by Jaaskelainen before Morrison was again denied by the bar when his thumping header clattered the woodwork. But both sides were forced to settle for a share of the spoils, as Albion failed to leapfrog Everton and move back into the top five.