Jose Mourinho's side fell at the Amex Stadium as Pascal Gross scored a 57th-minute header for the game's lone goal.
A first win for the Seagulls over United saw them guarantee themselves a place in the Premier League for next season, and also capped a season of frustration against promoted sides for the Red Devils.
With the defeat, United have now lost three league matches in a season against newly promoted clubs for the first time since the 1989-90 season.
The Red Devils have lost away to all three promoted sides in 2017-18: a 2-1 defeat at Huddersfield in October, a 1-0 loss at Newcastle in February and Friday's 1-0 reverse at Brighton.
The trio of losses marks the first time in United history they have lost away against the three promoted sides in a single top-division campaign.
Additionally, Mourinho's men are the only side to lose a Premier League game to all three promoted clubs this season.
Despite Friday's bad news United are still in pole position to finish second place in the league, carrying a five-point lead over Liverpool with two league games remaining.