Harry Maguire's 118th-minute winner saw Manchester United squeeze past a valiant Norwich City and into the semi-finals of the Emirates FA Cup.
Norwich played for half an hour with ten men following the dismissal of Tim Klose but, with a penalty shootout looming, Maguire was on hand to send his side to Wembley.
Norwich City 1-2 Manchester United (after extra time)
2019-20 Emirates FA Cup quarter-final
5.30pm BST, Saturday 27 June
Carrow Road, Norwich
United had taken the lead at Carrow Road six minutes into the second half when Odion Ighalo scored his third goal in the space of two cup appearances, before Todd Cantwell netted an excellent equaliser.
Klose's 88th-minute dismissal did not prevent Norwich from forcing the tie into extra time, but ultimately they could not hold out.
The tie was the first FA Cup match ever to be played in June, with the quarter-finals beginning 114 days after the fifth round had been completed due to a three-month suspension in professional football following the outbreak of COVID-19.
The hosts retained seven of the players who started their previous Emirates FA Cup tie, a fifth-round shootout victory over Tottenham Hotspur almost four months ago.
United, meanwhile, were virtually unchanged from their win against Derby County in the previous round, with only Maguire – who was ruled out of that game at Pride Park by illness – coming into the team.
Before kick-off, the two sides paused to pay tribute to work of the National Health Service with a minute's applause before taking the knee in support of the Black Lives Matter movement.
The opening quarter – punctuated by the first of two water breaks, a new introduction to the competition with ties running into June and July for the first time – was without much in the way of goalmouth action, as the teams contended with windy conditions.
United moved into the ascendancy in the latter part of the first half, although they failed to trouble Norwich goalkeeper Tim Krul. Instead it was the home side who had the first and only chance of the opening period, when Lukas Rupp and Emiliano Buendia saw shots desperately blocked by Maguire and Luke Shaw respectively before the lively Cantwell blazed over.
The tempo rose following the interval and United's breakthrough arrived soon afterwards, as Ighalo poked the ball past Krul from close-range after Shaw's cross had been sliced into the air by a combination of Juan Mata and Norwich captain Klose.
Norwich responded well, and looked set to equalise when Alexander Tettey got on the end of Buendia's excellent free-kick only for it to hit unwitting team-mate Ben Godfrey as it headed towards goal.
Their equaliser arrived in spectacular style with 15 minutes left on the clock, when Cantwell drove a swerving shot beyond Sergio Romero from 20 yards out.
The equaliser prompted United boss Ole Gunnar Solskjaer to introduce Paul Pogba and Nemanja Matic, and the former immediately went close to teeing up another substitute in Mason Greenwood, but the youngster fired wide.
Norwich then took hold of the game, with Buendia flashing an effort just off-target while substitutes Josip Drmic and Onel Hernandez also threatened the United goal.
With the Canaries looking good value to grab a winner, they were dealt a blow on 88 minutes when skipper Klose was dismissed for wrestling down Ighalo after he was sent in on goal by Bruno Fernandes.
United almost won it in the last of the six minutes' injury time awarded by referee Jon Moss, with Krul stopping Pogba's shot with his leg before getting up to turn Greenwood's follow-up wide.
The away side began extra time on the front foot, with Fernandes' deflected effort almost being flicked in by Pogba within 60 seconds of the restart.
Krul then tipped Rashford's dipping shot over the bar, but Norwich then recovered the resolve they had been forced to show since Klose's dismissal.
Having found their way to the halfway point of extra time, Farke's side immediately came back under pressure as Marcus Rashford had a shot was blocked and Fernandes drove over Krul's crossbar.
The Dutch goalkeeper then made a heroic save when he clawed out Maguire's header from a corner, before Fernandes – the taker of that set-piece – was also denied by an outstretch palm.
But there was nothing Krul could do when, in the 28th minute of extra time, Maguire was on hand to prod the ball into the net and break Norwich hearts.
United now go into Sunday's semi-final draw as they aim to win the Emirates FA Cup for the thirteenth time in their history and potentially equal the record held by Arsenal.
Norwich City: 1 Tim Krul, 2 Max Aarons, 4 Ben Godfrey, 7 Lukas Rupp, 12 Jamal Lewis, 14 Todd Cantwell, 15 Timm Klose (captain), 17 Emiliano Buendia, 22 Teemu Pukki, 23 Kenny McLean, 27 Alexander Tettey
Substitutions: 11 Onel Hernandez for Rupp 62', 20 Josip Drmic for Pukki 71', 19 Tom Trybull for Cantwell 90', 25 Ondrej Duda for Buendia 91', 35 Adam Uche Idah for Lewis 119'
Unused substitutes: 33 Michael McGovern (GK), 8 Mario Vrancic, 10 Moritz Leitner, 18 Marco Stiepermann
Goal: Cantwell 75'
Red card: Klose 88'
Manager: Daniel Farke
Manchester United: 22 Sergio Romero, 3 Eric Bailly, 5 Harry Maguire (captain), 8 Juan Mata, 14 Jesse Lingard, 17 Fred, 18 Bruno Fernandes, 20 Diego Dalot, 23 Luke Shaw, 25 Odion Ighalo, 39 Scott McTominay
Substitutions: 53 Brandon Williams for Dalot 62', 10 Marcus Rashford for Lingard 63', 26 Mason Greenwood for Lingard 63', 6 Paul Pogba for Fred 78', 31 Nemanja Matic for McTominay 78', 9 Anthony Martial for Bailly 96'
Unused substitutes: 1 David De Gea (GK), 15 Andreas Pereira, 24 Timothy Fosu-Mensah
Goals: Ighalo 51' & Maguire 118'
Yellow card: Fernandes 109'
Manager: Ole Gunnar Solskjaer
Referee: Jonathan Moss