Victor Lindelof scored the decisive spot-kick as Erik ten Hag’s team won 7-6, following a miss by Solly March, staying on course for a domestic cup double.
The semi-final in front of a crowd of more than 81,000 finished 0-0 after extra-time, with neither side showing the cutting edge required to break the deadlock.
The result means United will have the chance to derail City’s bid to match their unique achievement of winning the treble of Champions League, Premier League and FA Cup in the first-ever meeting between the rivals in an FA Cup final.
But the Red Devils, who won the League Cup earlier this season to end a six-year trophy drought, will have to find better form if they are to compete with Pep Guardiola’s red-hot team.
“On Thursday I saw a team I didn’t recognise but today we went back to usual,” Ten Hag told the BBC, referring to their Europa League horror show against Sevilla.
“I could see determination and resilience. We fought for every yard and competed in every battle. We had good chances.”
Luke Shaw came in at centre-back for the suspended Harry Maguire, with Marcus Rashford and Bruno Fernandes replacing Jadon Sancho and Marcel Sabitzer following Thursday’s 3-0 defeat in Spain, which meant a 5-2 defeat on aggregate in the Europa League quarter-finals.
Brighton, who lost the FA Cup final replay to United 40 years ago, had won the past two league fixtures between the sides and came to Wembley on a high after beating Chelsea last week.
The south-coast club settled first and had an early sight of goal when Kaoru Mitoma was brought down clumsily on the edge of the box by Antony in the sixth minute.
Argentine World Cup winner Alexis Mac Allister hit a fine curling effort that David De Gea did well to keep out before Julio Enciso flashed a shot wide.
Roberto De Zerbi’s Brighton were dominating possession, with United apparently content to sit back and try to exploit the pace of Rashford and Antony.
Brighton goalkeeper Robert Sanchez beat out a Fernandes effort in United’s first meaningful attempt on goal.
The massed ranks of Brighton fans were keen to play on the nerves of De Gea whenever the ball landed at his feet following a nightmare game for the Spaniard in Seville.
United, for long periods scrappy, produced a flurry of chances shortly before half-time, with Fernandes, Anthony Martial and Christian Eriksen failing to convert.
Brighton were quickly out of the blocks at the start of the second half. Enciso forced De Gea into a smart save before former United forward Danny Welbeck headed over from the resulting corner.
But neither side could break the deadlock and referee Craig Pawson blew for extra-time.
The game became stretched, with half-chances at both ends but there was still no breakthrough for either side despite multiple changes.
United top-scorer Rashford, who struggled to hit top gear, flashed wide with 10 minutes to go before De Gea cleared following a goalmouth scramble at the other end.
A high-quality shootout took place in front of the massed ranks of the Brighton fans.
United substitute Sabitzer stepped up to take his spot-kick with United 5-4 down and his heart would have missed a beat as Sanchez got his hand to it but he could not keep it out.
Brighton’s Adam Webster and United’s Wout Weghorst both scored before March’s painful miss with the 13th kick gave defender Lindelof a chance he did not squander.
Ten Hag praised “cool” Lindelof and Shaw - first-choice central defenders Lisandro Martinez and Raphael Varane are out injured - and said he was impressed by the performance of De Gea.
“He made some brilliant saves,” he said. “It hurt when he made mistakes on Thursday.
“Often when you make mistakes as a keeper you get punished. We let him down, we didn’t fight back for him. We bounced back today though.”
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