United took the lead early through Shea Lacey and a minute later Mason Mount extended it to 2-0.
At that point, the home team was in complete control of the match.
But Brighton were reduced before the end of the first half. Then, in the second, it was 2-2 and when Maxim De Cuyper made it 3-2, the turnaround was complete.
Marcus Rashford had a great chance to equalise, but the 3-2 stood and Brighton are through to the cup.
National team midfielder Yasin Ayari started on the bench but came on in the second half.
