Albion trail in-form Manchester United at half time through a Paul Pogba penalty – and a second goal added by Marcus Rashford.
Albion’s top scorer Glenn Murray missed a glorious chance to equalise before Rashford found the net.
The first real chance of the game fell to Brighton with eight minutes on the clock as they pushed into United’s half for the first time.
Unfortunately, Jurgen Locadia played a weak shot straight to the Reds’ goalkeeper David De Gea.
The Seagulls are, however, likely to be more concerned about upcoming home games against Watford, Burnley and Huddersfield Town.