Burnley reached their first FA Cup quarter-finals since 2003 when substitute Connor Roberts scored in the 90th minute to end the brave resistance of 10-man Fleetwood.
Vincent Kompany cut a frustrated figure on the touchline as his runaway Championship leaders squandered a host of chances despite Cian Hayes being dismissed on the stroke of half-time.
But not for the first time this season, The Clarets struck late to gain victory.
Charlie Taylor’s shot was parried by overworked Fleetwood goalkeeper Jay Lynch and when the ball was recycled into the penalty area Welshman Roberts got the faintest of touches to Vitinho’s shot – appropriately so on St David’s Day.
It was the least Burnley deserved for their 80% possession and 25 shots. But League One Fleetwood did their manager Scott Brown proud by coming so close to a fifth consecutive clean sheet.
Connor Roberts’ late goal secured a narrow victory over League One Fleetwood Town
Roberts flicked home from close range in the last minute to book place in the last eight
Fleetwood forward Cian Hayes was sent off for a high challenge on Josh Cullen
Burnley, making five changes, dominated the first half with Lyle Foster, Taylor and Scott Twine going close and Aristote Nielsa almost scoring a comical own goal with an errant backpass.
The home side also gained a boost moments before the interval when Hayes chased a bouncing ball and caught Josh Cullen with a high boot and knee.
The Irish teenager looked distressed at being given a red card and his team-mates protested because Cullen had been stooping when he was caught high in the chest.
Amazingly, Burnley still couldn’t score even though Kompany made a triple change after an hour with top scorer Nathan Tella among the new arrivals.
Taylor thought he’d scored when his header struck Harrison Holgate on the line. It looked extremely close but the referee’s watch didn’t bleep.
Fleetwood thought they’d made extra-time but Burnley have made a habit of finding a way and Kompany’s men, unbeaten in 15 games in all competitions, march on.