Bruno Fernandes scored a winning penalty for Manchester United with the final kick of the game after Brighton had equalised in the 95th minute.
Solly March's close-range finish looked to have given Albion a 2-2 draw, the least they deserved from a match they dominated and hit the woodwork in on five separate occasions.
Graham Potter's side also had a second-half penalty decision overturned by VAR with the score 1-1.
Brighton had earlier taken a well-earned lead in the 40th minute, Neal Maupay converting from the spot after Tariq Lamptey was tripped by Fernandes, but it lasted only three minutes as Lewis Dunk turned into his own net under pressure.
Marcus Rashford then struck just before the hour with a brilliant individual goal before the incredible late drama, which saw United given a penalty on VAR for a Maupay handball.
United survived an early scare when Leandro Trossard beat David de Gea from the edge of the box in the ninth minute, only to see his effort rattle the left post.
Brighton were playing with plenty of confidence and Trossard struck the woodwork for a second time in the 21st minute.
The Belgian again found space on the edge of the box, with his low effort flicking the outside of the right post after United’s defence stood off.
After Albion struck the frame of the goal for a third time through Adam Webster’s looping header against the crossbar, United thought they had taken the lead.
🔥 Oh Neal Maupay...that is WONDERFUL!
— Sporting Life Football (@SportingLifeFC) September 26, 2020
👀 David De Gea is not happy with the Brighton striker's cheeky penalty.#BHAFC | #BHAMUN pic.twitter.com/mt4FbRz5TW
Mason Greenwood thumped home past Mat Ryan but the strike was ruled out for offside against Rashford in the build-up.
Brighton deservedly went ahead five minutes before half-time through a cheeky penalty from Maupay.
Maupay, who scored twice at Newcastle last weekend, chipped the ball home from the spot after Fernandes was penalised for a challenge on Lamptey.
The Seagulls’ lead lasted less than three minutes as United captain Maguire – under pressure from defender Lewis Dunk – appeared to prod home from close range to make it 1-1 after Matic turned a Fernandes free-kick back across goal.
Brighton were awarded a second penalty of the afternoon within two minutes of the restart.
👏 Sensational stuff from Marcus Rashford!
— Sporting Life Football (@SportingLifeFC) September 26, 2020
😵 Ben White is going to be feeling dizzy after that...#MUFC | #BHAMUN pic.twitter.com/9338qjpOqN
But, after initially penalising Paul Pogba for a trip on Aaron Connolly, referee Chris Kavanagh reversed his decision after watching the incident on a pitchside monitor.
Minutes later it was United’s turn to be thwarted by VAR. Rashford turned the ball into the net but, despite the flag not initially going up, he was clearly offside.
However, Rashford was not to be denied for long as he put Solskjaer’s men 2-1 up soon after with a fine individual effort.
Brighton pressed for an equaliser in the closing stages – and got their reward.
👀 And here it is...
— Sporting Life Football (@SportingLifeFC) September 26, 2020
😱 Christopher Kavanagh awards Manchester United a penalty AFTER he's blown the full-time whistle!#BHAMUN pic.twitter.com/dBoSWWthAk
After the unlucky Trossard struck the woodwork for a third time in the match, then saw a close-range effort denied by De Gea, an unmarked March headed in a cross from Ali Jahanbakhsh in the fifth minute of added time.
However, there was further drama when Maupay was penalised for handling a Maguire header goalwards.
Fernandes dispatched the spot-kick emphatically, giving United a 3-2 victory with the final kick of the contest – in the 10th minute of added time.
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