Albion moved up to seventh after their first Premier League goalless draw since October 2022, but will feel they should have left the London Stadium with all three points.
Alphonse Areola was much the busier keeper in a game of few clear-cut chances, twice denying Pascal Gross at close range before making a fine save at full stretch to keep out Adam Lallanaâs fiercely struck shot late on.
Albionâs last league stalemate was 48 games ago against Nottingham Forest but apart from lack of a cutting edge there was little wrong with the performance.
Pervis Estupinan puts Bukaya Sako under pressure.
Adam Webster, who was making only his seventh appearance of the season and first since November 12, was one of two changes to the team that beat Spurs 4-2 last Thursday with Pervis Estupinan making his first league start since September.
Webster certainly saw plenty of the ball in the opening stages as Albion dominated possession, but it wasnât until midway through the first half before either keeper was tested.
Areola readjusted his possession to grab Facundo Buonanotteâs long-range strike before Jason Steele was twice called into action inside a minute. The Albion keeper didnât know that Jarrod Bowen was offside when he latched onto James Ward-Prowseâs pass and fired towards the far post but Steele got a touch to take it onto the post. He then blocked Ward Prowseâs close-range volley with an outstretched left leg. It was West Hamâs last clear-cut chance of the night.
Adam Webster had three first-half efforts but couldn't find the target.
Albion went close again on the half hour. Danny Welbeck headed skipper Pascal Grossâs free kick across the face of goal to Jack Hinshelwood, and his volley on the turn was blocked by Areola.
Albion should have scored two minutes before the break. Welbeck fed James Milner, who was equalling Ryan Giggs' 632 Premier League appearances, on the left. His lovely cross picked out Grossâs late run perfectly, but the German directed his header straight at Areola when anything either side would have been a goal. Â
Referee Sam Borrott ignored penalty appeals early in the second half when a prostrate Emerson seemed to block Buonanotteâs cross with his arm and the Argentinian was involved again when Albion threatened on 54 minutes. His pass opened up space for Welbeck to take aim with his right foot from 12 yards but Areola made another good reflex save.
James Milner will join Ryan Giggs on 632 Premier League appearances if he plays against West Ham.
The Hammersâ keeper made another intervention on the hour after great play by Joao, who slalomed across the face of goal from the left but his shot was too close to Areola.
Albion seemed to be getting on top then West Ham briefly roused themselves. Tomas Soucek stabbed a close-range shot wide of the far post after a deflection on Said Benrahmaâs cross took the ball into his path.
Evan Ferguson replaced Welbeck midway through the half and nearly made an immediate impact when he controlled Buonanotteâs pass with his left foot and take the ball over Edson Alvarez to create space for a shot with his right which was half a yard wide.
Joao Pedro was denied by Casemiro's goalline clearance in the second half.
Albion kept pushing. Gross met Milnerâs cross with a header that lacked power and drifted wide; Lallanaâs shot was blocked by Soucek after fellow sub Jakub Moder set him up; Ferguson nearly converted Lallanaâs lay-off but Angelo Ogbonna stretched to make an important block then Moder, on the stretch, couldnât keep his volley down after Joao and Milner combined down the left.
Areola saved his best until last, flinging himself to his right to push away Lallanaâs powerful strike with inside the D before flopping on Hinshelwoodâs looping header in the last action of the game. Only one side had looked like winning for long spells, but Albion had to settle for maintaining their unbeaten Premier League record at the London Stadium.
Albion: Steele, Hinshelwood, van Hecke, Webster (Moder 75), Estupinan; Milner, Gross, Gilmour; Buonanotte (Lallana 75), Welbeck (Ferguson 66), Joao.
Subs not used: Verbruggen, Dahoud, Baleba, Samuels, Baker-Boaitey, Kavanagh.
Referee: Sam Barrott