Albion trail to a James Ward-Prowse goal after a mistake by Adam Webster.
Ward-Prowse’s first Hammers goal was a scrappy one, but it went in, past Albion debut keeper Bart Verbruggen.
The Seagulls have dominated the remainder of the game but have yet to really trouble Alphonse Areola – although Areola did drop the ball in the six-yard box but Albion couldn’t capitalise.
Billy Gilmour went closest for Albion with a low shot that skimmed the post.
Albion have looked impressive with Pascal Gross and Kaoru Mitoma looking particularly effective.