The hosts continued to pick holes in the United defence and piled on the pressure, but could not add to their tally.
United attempted to fight back but a strong goalkeeping performance from Robert Sanchez kept them out.
United have now conceded 56 goals in the Premier League this season, their worst defensive record in a single campaign in the competition.
The result means it is now mathematically impossible for sixth-placed United to qualify for the Champions League, as they sit five points adrift of fourth-placed Arsenal with one game left to play.
Brighton are ninth, five points off a Europa Conference League spot with two remaining matches.