
Solly March, Brighton’s seventh player to step up to the spot in the shootout, launched the ball over the bar, before Victor Lindelof found the net to secure a 7-6 shootout victory for United.
The nail-biting finale was a fitting ending after 120 goalless minutes of wild swings in a game that careened from end to end all night.
Treble-chasing Manchester City await in the final after they beat Sheffield United 3-0 in their semi on Saturday.
Sunday’s semi was a rematch of the 1983 final, when Brighton lost to United in the south coast side’s only appearance in the showcase game.
Erik ten Hag’s United, 12-times FA Cup winners, are chasing a cup double after winning the League Cup in February.
The FA Cup final is on June 3 at Wembley.