The impressive Marcus Rashford fired in from a tight angle which Brighton goalkeeper Jason Steele did well to keep out at his near post.
Argentina’s World Cup winner McAllister shot wide of De Gea’s goal, while Anthony Martial’s effort at the other end was pushed back by Steele.
De Zerbi’s side were on top again in the early stages of the second half but Mitoma and Danny Welbeck were guilty of wasting openings.
As the half wore on the game became more fearsome, suiting United, who were struggling to find flow, but Brighton finished the stronger of the two teams.