A spirited performance from the Hammers will also give Avram Grant some breathing space as he faces up to the prospect of the chop.
Mark Noble scored the first early on before Liam Ridgewell equalised for Birmingham just after half-time. The Hammers were then reduced to 10 men when Victor Obinna was sent off for kicking out at Sebastian Larsson.
Carlton Cole then scored a break-away goal with a scuffed shot that slipped through the legs of Ben Foster with only ten minutes left.