Things nearly got worse for West Ham after 63 minutes when JonathanGreening delivered a low cross from the left, but Gareth Southgate's shot went narrowly wide.
Veteran midfielder George Boateng provided a decent platform sitting in the centre of the midfield and fellow new signings JonathanGreening and Andy Reid showed glimpses of their undoubted guile and creativity.
Liverpool striker Fernando Torres inadvertently flicked on a corner to JonathanGreening at the far post but the Baggies skipper saw his first-time shot saved and the rebound blocked by the legs of Reina.