Substitute Khadra won an entertaining contest when United broke clear deep in stoppage time.

The win extends the Blades' unbeaten Championship run to eight games.

Swansea drop to 21st having lost on a night when a draw probably would have been the fairest outcome.

Russell Martin's side went toe to toe with the early-season pacesetters, but - not for the first time this season - they were undone in injury time.

United's fifth victory in their last six league outings - and their first at Swansea since 1958 - means they are four points clear of second-placed Norwich City.

The game was preceded by a minute's silence in memory of Queen Elizabeth II, though Swansea opted not to play the national anthem.

When the football got under way, it was the visiting fans making the early noise as Sander Berge crossed for the unmarked Rhys Norrington-Davies, only for his header to be gathered by goalkeeper Steven Benda.

Paul Heckingbottom's side were soon threatening again, with George Baldock's inviting centre lifted narrowly over the bar by a sliding McBurnie.

Swansea eventually settled, and might have gone in front when Piroe stepped away from his marker in the penalty area only to shoot too close to Wes Foderingham.

Next Piroe almost exposed a sleeping United defence at a throw-in, but Ryan Manning could not make proper contact with the Dutchman's pull-back.

United striker Iliman Ndiaye then had a chance at a corner only for his shot to ricochet wide off Nathan Wood, before Swansea carved the first opportunity of the second period as Matty Sorinola sliced wide at the far post.

Piroe was soon involved again, turning beautifully once more but firing wide, only for United to hold heads in hands at the other end as Berge shot over from point-blank range.

Sander Berge shields the ball from Swansea's Joe Allen

There was no shortage of entertainment despite the lack of goals, with Swansea's next big moment coming when a Foderingham clearance hit his own defender and dropped to Ollie Cooper.

He looked to square when he really ought to have shot himself, with Piroe snuffed out by Baldock's recovery challenge.

United looked to have blown their chance to win it late on when Khadra crossed for fellow substitute Brewster only for the ex-Swansea loanee to flash a header wide.

But in the fourth minute of added time, Brewster broke clear - with Swansea appealing in vain for a foul on Kyle Naughton - and squared for Khadra to guide home the winner.

Swansea head coach Russell Martin:

"It was a really good game. We didn't start very well, but I was really pleased with our reaction, we looked really dangerous, on the counter in particular.

"We have to make the most of the big chances we had. We're 45 seconds away from everyone feeling positive against a team who are top of the league and free-scoring. We went toe to toe with the team at the top of the league, the players were great for so long and we end up getting beaten.

"I trust Kyle. He's clipped his heels. The boy's not meant to but Kyle has run across him.

"It is a foul. It's the easiest decision the referee has got to make all night. It's the 94th minute, the guy's running back towards his own goal, he clips his heels, just give the free-kick. It's really not difficult."

Sheffield United manager Paul Heckingbottom:

"It's why we love it. It's better when it goes for you, those last-minute winners, believe me.

"You have got to make the most of it when you win a game like that. There will be a game when it goes the other way, so you have got to enjoy it.

"We gave Swansea three good chances. There were three real good tackles. The final one was from Bash (Chris Basham) and we scored about eight seconds later.

"I didn't think it was a foul [before the goal]. I think Kyle [Naughton] realised he was in a foot race and he was going to get beaten. He tried to step across Rhian [Brewster]. What Rhian's done well, he put the brakes on and jumped so there was no contact.

"But I would have complained if I was Russ, course I would, but it's not a foul."