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:
. LONDON, ENGLAND - APRIL 23: Marcel Sabitzer, Victor Lindelof and Diogo Dalot of Manchester United celebrate after the team's victory in the penalty shoot out during the Emirates FA Cup Semi Final match between Brighton & Hove Albion and Manchester United at Wembley Stadium on April 23, 2023 in London, England. (Photo by Mike Hewitt/Getty Images)
Marcel Sabitzer, Victor Lindelof and Diogo Dalot of Manchester United celebrate after the team's victory in the penalty shoot out during the Emirates FA Cup Semi Final match between Brighton & Hove Albion and Manchester United. (Photo by Mike Hewitt/Getty Images) Photo: Mike Hewitt
. David de Gea - 7
Bounced back well from his horror show at Sevilla. Made a couple of fine saves to keep the scores level. Could have come off his line more to help his defence out. Didn't need to make any saves in the shoot-out, in the end, as March blasted over the bar. But six penalties were scored against him. (Photo by GLYN KIRK/AFP via Getty Images) Photo: GLYN KIRK
. Aaron Wan-Bissaka - 8
Outstanding. It was an intriguing battle against Mitoma and he kept the blistering Japanese forward quiet - which is no mean feat. Attacking contribution improved as game went on. Replaced by Malacia in injury-time. (Photo by GLYN KIRK/AFP via Getty Images) Photo: GLYN KIRK
9. Bruno Fernandes - 5
Started the game well, full of confidence after his exploits for Portugal. Booked for tackle from behind on Dahoud. No impact in the second half Photo: Michael Regan/Getty Images
10. Christian Eriksen - 5
Superb bit of skill to beat Dahoud early on. Some sloppy passing came into his game and wasted set piece opportunities. His impact was limited Photo: Ash Donelon/Manchester United via Getty Images
11. Marcus Rashford - 6
Looked sharp early on as United came out of the blocks quickly. Rashford was unlucky not to score or at least have an assist to his name after VAR intervened. He was however very wasteful throughout the game. Could have looked for a pass to Hojlund instead of shooting every time he had a sight of goal. A couple of sloppy passes late on and didn't always close down his man quick enough Photo: Michael Regan/Getty Images
12. Rasmus Hojlund - 7
The fans were furious when he was substituted. He looked the most likely player to score and was desperately unlucky not have a goal on his full debut after being denied by VAR. It was a nice finish by the 20-year-old, who put himself about well and linked up nicely with Rashford Photo: OLI SCARFF/AFP via Getty Images