Albion are level with United but could be a least two goals in front.
Leandro Trossard has hit the post twice, both the left and right-hand uprights.
And a header from Adam Webster was tipped on to the crossbar by David de Gea.
Tariq Lamptey won a penalty for the Seagulls after being clumsily bundled over by Bruno Fernandes.
Neal Maupay hit a sublime chipped ball from the spot to put the Seagulls in front, with 40 minutes played.
Nemanja Matic appeared to strike Aaron Connolly in the face from the restart but received only a yellow card.
Minutes after Albion went in front, Harry Maguire and Lewis Dunk tussled in the six-yard box from a United free kick.
The ball clipped off the Brighton skipper’s heel to make it 1-1 moments before the break.
