Albion are behind at Old Trafford to a Romelu Lukaku header on 37 minutes although Albion have had slightly more possession.
Lewis Dunk went close for Brighton with a header and Ezequiel Schelotto saw a cross shot drift narrowly wide.
Before the goal, Juan Mata went close for United and Chris Smalling hit the outside of the post.
Albion have looked composed and shown some clever attacking play.
Leo Ulloa, Jurgen Locadia and Solly March have all been linking up well.
The match started in a blizzard and snow was still evident on the Old Trafford pitch as the half-time whistle was blown.