Pascal Gross headed straight at Alphonse Areola from a superb James Milner cross as Albion dominated possession in the first half.
Albion keeper Jason Steele had to be alert and made a good save from James Ward-Prowse while Tomas Soucek saw a shot touched on to the post by Steele.
A storming run from Facundo Buonanotte from almost his own half to the West Ham penalty area saw him win a free kick – which eventually came to nothing.
And Danny Welbeck sent a header goalbound from a set-piece but Areola again pulled off an impressive save.
Jack Hinshelwood had a stab seconds later but the Hammers keeper was alive to the danger.
The only card of the half was a yellow shown to Ben Johnson for tripping.
Brighton were brilliant throughout in this game. As dominant a performance as any team have given in this season’s campaign. Everyone excelled, just a pity the ball would not go in the net.