Robbie Brady sent Burnley through to the fourth round of the Carabao Cup on a dramatic evening at Turf Moor.
David McGoldrick had given Sheffield United a fourth minute lead, but Matej Vydra levelled for the hosts midway through the second half.
Oli McBurnie had replaced McGoldrick five minutes before Burnley's equaliser, and it was the Scot's missed spot kick that proved decisive.
Chris Wood, Vydra, Josh Brownhill and Erik Pieters had all converted, before Brady slotted the ball to the right of Wes Foderingham.
Burnley's reward is a 3rd round trip to Millwall. Should they survive The Den, Sean Dyche's side will be at home to either Manchester City or Bournemouth.
Wolves became the third Premier League casualty of the 3rd round, going down 1-0 at home to Michael O'Neill's Stoke City.
While Brighton thrashed League One Portsmouth 4-0 at the Am-Ex to set up a 3rd round date with Preston at Deepdale.
Carabao Cup 3rd round draw:
Lincoln City v Liverpool
Bristol City v Aston Villa
Chelsea v Barnsley
Fleetwood Town v Everton
Preston North End v Brighton & Hove Albion
Fulham v Sheffield Wednesday
Leicester City v Arsenal
Leyton Orient v Tottenham Hotspur
Luton Town v Manchester United
Manchester City v Bournemouth
Millwall v Burnley
Morecambe v Newcastle United
Newport County v Watford
West Bromwich Albion v Brentford
West Ham United v Hull City
Stoke City v Gillingham
Carabao Cup 4th round draw:
Lincoln City or Liverpool v Leicester City or Arsenal
Millwall or Burnley v Manchester City or Bournemouth
West Brom or Brentford v Fulham or Sheffield Wednesday
Fleetwood Town or Everton v West Ham United or Hull City
Bristol City or Aston Villa v Stoke City or Gillingham
Leyton Orient or Tottenham Hotspur v Chelsea or Barnsley
Newport County or Watford v Morecambe or Newcastle United
Preston North End or Brighton & Hove Albion v Luton Town or Manchester United