Despite making a bright start, United fell behind in the 20th minute when Danny Welbeck slotted home against his former club when left unmarked in the penalty area.
United responded well and thought they had levelled just before the break through big-money signing Rasmus Hojlund, on his full debut, but the ball was adjudged to be out of play when Marcus Rashford pulled the ball back to the Dane.
Brighton fully capitalised on that VAR reprieve, however, as fine goals from Pascal Gross early in the second half and a João Pedro strike brought groans of dismay all around Old Trafford.
Substitute Hannibal Mejbri did get one back for the hosts with 18 minutes left but Brighton held on with ease to move up to third in the standings on 12 points from five matches. United dropped to 12th on six points.