Michael Carrick's side led 2-0 inside ten minutes, only for the Seagulls to score three times in the second half and complete one of the more remarkable collapses seen at the ground in years, BBC Sport reported.
It leaves Manchester United with three straight domestic cup exits, and the manager under fresh scrutiny just three days after a derby defeat by 10-man Manchester City.
Academy graduate Shea Lacey marked his first senior start with a composed finish inside eight minutes, and Mason Mount doubled the lead soon after, converting the rebound from a blocked Marcus Rashford effort.
Charalampos Kostoulas pulled one back for Brighton before half-time, then levelled matters himself early in the second period, ghosting away from his marker to turn and fire beyond debutant goalkeeper Karl Darlow. Kostoulas quickly turned provider too, teeing up substitute Maxim De Cuyper to complete the turnaround.
Carrick sent on captain Bruno Fernandes with 18 minutes left in search of a way back, but Jason Steele kept out Rashford at the other end and United could not respond, with the home crowd booing their side off at the final whistle.
Losing after leading 2-0 at home hadn't happened to Manchester United since 1976, when Tottenham overturned an identical deficit to win 3-2 — a gap of exactly half a century. Wednesday's defeat also follows last season's shock exit at League Two Grimsby and January's FA Cup loss to Brighton at the same stadium.
Everton needed only a handful of minutes from a substitute to see off a much-changed Wolverhampton Wanderers. Carlos Alcaraz had barely entered the fray when he cut inside from the right and slotted home in the 80th minute, sending David Moyes' side through and stretching their unbeaten start to the season to six matches.
The goal was Alcaraz's first for the Toffees since he last scored in the competition 13 months earlier, and it came against a Wolves side that has since been relegated to the Championship.
Former Everton goalkeeper João Virgínia, handed a start against the club he left for Sporting in 2025 after seven years on Merseyside, was the busier of the two keepers for long spells, denying Thierno Barry from close range before the interval. Everton's reward is a home draw against Newcastle United in the week commencing 26 October.
Aston Villa were equally untroubled in the end, beating Coventry City 3-1 as Tammy Abraham's early opener and second-half strike sandwiched a Ross Barkley header.
Abraham, recalled among seven changes to the side beaten by Nottingham Forest at the weekend, had scored only once in his previous 16 appearances before Wednesday. He had extra reason to press his case: the striker turned down loan exits to Ipswich Town and Everton in the summer after Unai Emery indicated he was willing to let him go, and has since watched the club spend £65 million on Nicolas Jackson from Chelsea.
Coventry, whose season is unravelling, briefly threatened a shock through a fine Victor Torp free-kick but could not build on it, slipping to a fifth defeat in their opening six games.
For Villa and Everton, round three offered rare good news after difficult starts to the campaign. For United, it was another chapter in a cup record that is fast turning into a crisis.