The sides get to do it all over again in four days’ time as United are back at the Amex Stadium for an EFL Cup last-16 tie.
Brighton travel to Everton for their next Premier League outing in a week’s time, while United host Tottenham on their return to top-flight action.
What will quite possibly go down as the game of the season in the Premier League finishes 3-2 to Man United.
A Dunk own goal and Rashford’s strike put United ahead after Maupay had opened the scoring from the penalty spot.
Albion hit the post five times and equalised in stoppage time through March’s header, only for Fernandes to bury a penalty in the 100th minute of the game.
Brighton: Ryan, White, Dunk, Webster, Lamptey, Lallana (Gross 74), Alzate, March, Trossard, Connolly (Jahanbakhsh 74), Maupay
Subs not used: Steele, Bernardo, Burn, Veltman, Molumby
Goals: Maupay 40
Bookings: Trossard, White, Dunk
Manager: Graham Potter
Manchester United: De Gea, Wan-Bissaka, Maguire, Lindelof, Shaw, Matic, Pogba (Fred 65), Greenwood (Bailly 82), Fernandes, Rashford, Martial (van de Beek 90)
Subs not used: Lingard, Fosu-Mensah, Henderson, McTominay
Goals: Dunk OG 43, Rashford 55, Fernandes 90_10
Bookings: Fernandes, Matic
Manager: Ole Gunnar Solskjaer
United – needing a response to their limp opening-game loss to Crystal Palace – levelled within 187 seconds, though, Lewis Dunk unfortunate to divert past Mat Ryan from close range after Fernandes’ set-piece caused problems.
Referee Chris Kavanagh chalked off a penalty he had awarded early in the second half after reviewing the incident himself, allowing Paul Pogba to breathe a sigh of relief after Aaron Connolly took a tumble.
Ole Gunnar Solskjaer’s men made full use of the reprieve as Marcus Rashford, having just seen a goal disallowed, brilliantly danced his way into the box and fired home via a deflection off Dunk.
Graham Potter was cursing his luck when Solly March and Leandro Trossard hit the post and crossbar respectively, before jumping for joy when the former headed in a stoppage-time equaliser.
But the drama was not over and Maupay handled Harry Maguire’s header, which was cleared off the line by March, allowing Fernandes to wrap up the points from the spot in a game that will live long in the memory.