Erik ten Hag’s team had the better openings in the first half of the 1983 final rematch on Sunday with a rolling shot that went just beyond Roberto Sánchez’s right-hand post as Bruno Fernandes gave the Red Devils their finest opportunity at the opening of the 45 minutes.
Although, the Seagulls came back at the beginning of the second half, forcing David de Gea to stop Julio Enciso’s left-footed attempt following a corner scramble.
But as Man United kept withstanding pressure, Danny Welbeck flicked a header from Pascal Groß’s corner against his former team over the crossbar.
However, they immediately resumed their siege of Brighton’s goal as Sánchez blocked Antony’s errant attempt from outside the penalty area.
De Gea produced a full-length stretch to stop Solly March and Groß in rapid succession during the final phases of an end-to-end battle.
Extra time followed a similar pattern to the previous 90 minutes as both sides enjoyed a spell of dominance without fashioning real chances.
Marcus Rashford threatened to break the cycle with a deflected effort which drew a superb stop from Sánchez at his near post.
Brighton should have punished United’s slack defending but Kaoru Mitoma failed to steer the ball past De Gea.
As penalties beckoned, both teams converted to send the shootout into sudden death before Solly March skied his effort and Victor Lindelof converted.
United will now face Manchester City in the Wembley showpiece on 3 June.