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.