Burnley needed a 90th-minute goal from Connor Roberts to edge out 10-man League One Fleetwood 1-0 and advance to the quarter-finals of the FA Cup for the first time in 20 years.
Vincent Kompany's side played with an extra man for more than 45 minutes after Cian Hayes saw red in first-half stoppage time, but were in danger of being taken to extra-time by a Fleetwood side who showed why they had come into this match on the back of four straight clean sheets.
When the goal did come it was harsh on visiting goalkeeper Jay Lynch, who made fine saves from Halil Dervisoglu and Charlie Taylor in quick succession only to be beaten from close range as Roberts' flick diverted Vitinho's shot through a crowded area into the net.
It was reward for a Burnley performance that had seen them dominate possession all night and register 31 attempts at goal against a side playing in the fifth round for the first time.
The hosts were almost gifted an opener eight minutes in when an under-pressure Aristote Nsiala went to pass the ball back but did not check where Lynch was, sending the goalkeeper scrambling to hook it off the line.
That proved to be as close as Burnley got to a goal before the break as Scott Brown's men made them work.
Lyle Foster should have done better when he robbed Harrison Holgate of the ball on the halfway line and ran free towards goal. But the South African, still looking for his first Burnley goal, got his finish wrong as he chipped into the hands of a grateful Lynch.
The Burnley pressure was building as a couple of shots were charged down before the lively Vitinho blazed over, while Taylor had a pop from range but sent it high and wide before testing Lynch with a better effort the goalkeeper needed two opportunities to gather.
The ball then came to Anass Zaroury, who quickly controlled and got a shot away to force Lynch into a save to his right at the expense of a corner.
Fleetwood, barely seen as an attacking force, had a couple of opportunities from free-kicks late in the half but failed to create anything from either.
And things then changed in first-half stoppage time as Hayes crashed into Josh Cullen when challenging for a high ball, with Dean Whitestone's decision to show a red card appearing harsh on second viewing.
Reduced in number, Fleetwood retreated further into their shell after the break, packing the defence with players and frustrating Burnley's attempts to find a way through.
Zaroury flashed a shot into the side-netting in the 56th minute, then Lynch did well to deny Foster as he reacted quickest to a loose ball.
Burnley frustration grew as Scott Twine hit a free-kick into the wall after Scott Robertson fouled Cullen in the D.
Nathan Tella, whose double saw off Ipswich in the previous round, was one of three players to come on just after the hour. Roberts, another of the fresh faces, fired in a low cross for Tella, but his shot was blocked at the near post.
Moments later, Lynch got a hand to Taylor's header, taking just enough pace off it that Holgate could hook it off the line.
Lynch then clawed away shots from Dervisoglu and Taylor, but when the ball came back into the box, Roberts got the decisive flick.
Kompany: Mixed feeling on Man City return
Vincent Kompany is looking forward to an emotional return to Manchester City after Burnley were paired with his former club in the quarter-final draw.
Burnley face a match-up against Kompany's old boss Pep Guardiola and a club he captained to four Premier League titles and two FA Cups.
"It's a double feeling to be honest," Kompany said. "My ties are extremely strong with the club and that remains. The kids will have a tough decision to make on the day but it's one we are looking forward to.
"We've got a few games now which are more important, which is every Championship fixture between that game and now but it will be a special day. I think for the players, this is an experience and they've earned the right to look forward to such a game."
When City fixtures do not clash with Burnley, Kompany regularly takes his kids to a stadium where his statue stands outside. A warm reception will surely await off the pitch but not on it.
"From my side, I'm really calm about it," Kompany added. "I know that past the hugs and the high fives, there is a machine there that wants to win everything. We'll focus first on the Championship games and then give it the right place it deserves."
Fleetwood boss Scott Brown declared himself "very proud" of his players after they came within a few seconds of forcing extra-time.
"Obviously it's always going to be hard coming here with 11 men, so coming here with 10, the lads' understanding of the game plan was brilliant," he said. "We tried to frustrate them through the first half and we did that. We tried to catch them on the counter…
"In the second half, it gets harder, you get the ball and there's three or four players on you. You have to defend for your lives.
"Lynchy from start to finish was exceptional and he deserves man of the match with him behind our back five, the back five was solid. To take them all the way, the top Championship side with 10 men was exceptional and I couldn't be any more proud."
FA Cup quarter-final draw in full
Man City vs Burnley
Man Utd vs Fulham
Brighton vs Grimsby
Sheffield United vs Blackburn
FA Cup key dates
- Quarter-finals - Set to be played the weekend of March 18 and 19
- Semi-finals - Set to be played on the weekend of April 22 and 23
- Final - Saturday June 3
What's next?
Burnley face Blackpool at Bloomfield Road in the Sky Bet Championship on Saturday March 4; kick-off 3pm. Meanwhile, Fleetwood Town visit Cheltenham in Sky Bet League One at the same time.