Victor Lindelof scored the winning spot-kick after an epic shoot-out which saw 13 penalties scored.
It sets up an FA Cup final with city rivals Manchester City, who beat Sheffield United on Saturday (April 22).
It was a stop-start first-half, with Manchester United seemingly looking to slow the play down to hinder Brighton’s game-plan.
Albion were the better team but couldn’t fashion a great deal of goal-scoring opportunities in the opening 45 minutes. Alexis Mac Allister came closest with a superb free-kick that forced David de Gea into a flying save.
United rallied towards the end of the half and nearly took the lead through Bruno Fernandes.
It became an end-to-end encounter after the break but neither side could break the deadlock. De Gea was again called into action on more than one occasion, saving from Julio Enciso and Solly March. Danny Welbeck also missed a golden headed chance.
Extra-time was required and Brighton had Rob Sanchez to thank for keeping them in the game when he saved brilliantly from Marcus Rashford. Marcel Sabitzer also saw a header go wide.
Brighton looked like they might steal it at the end of the game but a heavy touch from Kaoru Mitoma let United off the hook.
De Gea saved again from Solly March late on and United had chances of their own but a penalty shoot-out was needed to separate the sides.
It was a case of who would blink first as every penalty was scored until Solly March blasted over the bar. Lindelof made no mistake to spark jubilant scenes among the United faithful.
Here is how we rated the Manchester United players:
1. Manchester United 1-3 Brighton
Manchester United’s month went from bad to worse as in-form Brighton continued their recent dominance against the Old Trafford club. Photo: OLI SCARFF/AFP via Getty Images
2. Onana - 5
No chance with Brighton's first two goals. Could have done better with the third, which he got a hand to. Incredible save to deny Ansu Fati a debut goal - one of four stops late on to keep the score down Photo: Ash Donelon
3. Diogo Dalot - 7
Perhaps a surprise to see him start over Aaron Wan Bissaka given the latter's ability to keep Kaoru Mitoma quiet in previous encounters between the sides. Dalot did well in a tough battle against the tricky Japanese forward, though. Some important tackles but not great positioning for third goal, beaten too easily by Tariq Lamptey. Lovely skill to beat Mitoma and played perfect pass to Rashford. Photo: Matthew Peters/Manchester United via Getty Images
4. Victor Lindelof - 4
Poor. Made fans nervous early on when he played a loose ball back to Onana. Couldn’t cope with Albion’s movement in forward areas Photo: OLI SCARFF