The hosts took the lead from the penalty spot after Bruno Fernandes fouled Tariq Lamptey. French striker Neal Maupay converted it coolly with a Panenka dink.
As Brighton looked set for a half-time lead, Fernandes put a cross into the box from a free-kick. Nemanja Matic touched the ball back in and Lewis Dunk put it into his own net after being pressured by United skipper Harry Maguire.
Ten minutes into the second half, United went in front through a wonderful goal from Marcus Rashford. Bruno fed the forward behind the home defence before the Wythenshawe man dribbled his way into the Brighton box.