CLICK HERE FOR THE MINUTE-BY-MINUTE UPDATES
Swansea City secured their first home win of the season in the Championship despite finishing the game with nine men following the sendings off of Jordi Lopez and Nathan Dyer.
But goals from substitutes Lee Trundle (penalty) and Tom Butler earned the brave Swans a superb victory against the high-flying Blades.
Swans: Dorus de Vries; Angel Rangel, Garry Monk(C), Alan Tate, Fede Bessone (Tom Butler, 56'); Jordi Lopez, Ferrie Bodde (Lee Trundle, 9'(Jazz Richards, 81')), Ashley Williams, Mark Gower, Nathan Dyer; Gorka Pintado.
Not Used:David Cornell (GK), Craig Beattie, Besian Idrizaj, Kerry Morgan.
Blades: Mark Bunn, Nick Montgomery, Chris Morgan (C), Matthew Kilgallon, Darius Henderson, David Cotterill, James Harper, Andy Taylor (Kyel Reid, 87'), Keith Treacy (Ched Evans, 28'), Stephen Quinn (Glen Little, 83'), Kyle Walker.
Not Used: Ian Bennet, Jordan Stewart, Andrew Davies, Jon Fortune.
Attendance: 14,324 Away: 549
Referee: D Deadman (Hertfordshire)
With midfielders Leon Britton (toe), Joe Allen (hamstring), Andrea Orlandi (thigh), Cedric van der Gunn (thigh) and Darren Pratley (shoulder) all out injured, there was a first start for Ferrie Bodde after a 10-month absence with a knee injury.
With such a shortage in the middle, central defender Ashley Williams also moved forward into the centre of the park. Alan Tate moved to partner skipper Garry Monk in the heart of the defence, with Fede Bessone coming in at left-back.
If the injury situation wasn't bad enough for manager Paulo Sousa, Bodde limped off after just nine minutes with what looked worryingly like a knee problem.
He was replaced by Lee Trundle as Swansea went with two up-front against a Sheffield United side sitting pretty in fifth place.
Despite all the injury disruptions, Swansea started confidently and had the edge in the first 20 minutes as Tate forced Mark Bunn into an early save with a header.
With neither side creating many openings, Nathan Dyer had the home crowd on their feet in the 29th minute when his quick feet took him clear and Bunn was forced to save a llow shot which was bound for the bottom corner.
Gorka Pintado was quick to follow up the shot before going down as Bunn dived on the rebound. The Swans fans were up claiming a penalty, but the referee quite rightly waved the appeals away.
As the half came to a close, Dorus de Vries still hadn't had a shot to save as Jordi Lopez curled an effort just wide of the Sheffield upright.
Swansea's luck turned for once seven minutes after the interval, however, as Lee Trundle fired the Swans ahead from the penalty spot.
Great work down the right by Dyer saw his low cross find Trundle on the edge of the area. And when Trundle's quick feet took him clear, he was bundled over by Nick Montgomery.
The referee pointed straight to the spot and Trundle picked himself up to fired coolly beyond Bunn before being mobbed by his team-mates.
Trundle kissed the badge all along the East Stand as the Swans were ahead.
Sheffield immediately stepped on the gas and looked to have grabbed a 58th minute equaliser when substitute Ched Evans followed up an effort from fellow Welsh international David Cotterill to bundle the ball home.
But the linesman's flag saved the day with an offside decision the visitor's were far from happy with.
But Sheffield were looking more dangerous as the game progressed and finally grabbed the equaliser in the 74th minute as the Swans started to give too much possession away.
James Harper was at the heart of the equaliser when his ball found Stephen Quinn inside the area and the midfielder flicked it beyond de Vries.
Three minutes later and the Swans were down to 10 men when Lopez picked up his second yellow card for a challenge on Evans.
Sheffield went for the kill, but Swansea stood tall and grabbed the winner themselves through substitute Tom Butler.
With eight minutes remaining, Ashley Williams found Dyer who laid a perfect ball off to Butler who rifled a superb low shot into the bottom corner from 22 yards for his first goal of the season.
Swansea found themselves down to nine men in injury time as Nathan Dyer was shown a second yellow card for kicking the ball away.
But despite six minutes of injury time, the Swans held on.