Swansea City's six-game unbeaten run on the road was ended at a bitterly cold Bramall Lane.
Wales international Ched Evans scored the only goal just before half-time as he shot beneath Dorus de Vries after latching on to Andy Reid's long pass.
Thisgame was far from being a Christmas cracker but the visitors did have their chances, especially at the start of the second-half, but Blades 'keeper Steve Simonsen was on form to stop everything that he had to deal with.
It was a disappointing afternoon in south Yorkshire as the Swans could have climbed up to second spot with a point.
Brendan Rodgers stuck with the same side that was held by Millwall eight days earlier.
The visitors included two former Blades in the starting eleven - ex-loanees Craig Beattie (pictured) and Nathan Dyer - while a third, David Cotterill, was named amongst the substitutes.
Sheffield United, meanwhile, handed a start to former Swan Leon Britton who lined-up against his ex-club for the very first time.
Blades:Steve Simonsen; Nyron Nosworthy, Jean Calve, Andy Taylor, Kyle Bartley, Stephen Quinn, Leon Britton, Nick Montgomery (C), Mark Yeates, Andy Reid (Jamie Ward, 78'), Ched Evans (Danny Batth, 90+3').
Not Used: Mihkel Aksalu (GK), Johnny Ertl, Lee Williamson, Rob Kozluk, Matthew Lowton.
Swans:Dorus de Vries; Angel Rangel, Garry Monk(C), Ashley Williams, Alan Tate; Mark Gower (Darren Pratley, 46'), Joe Allen, Andrea Orlandi; Nathan Dyer (David Cotterill, 67'), Scott Sinclair, Craig Beattie (Jermaine Easter, 46').
Not Used:Yves Makabu-Makalambay (GK), Neil Taylor, Kemy Agustien, Stephen Dobbie.
Referee: M P Russell (Hertfordshire)
You'd have to go right back to 1939 for the last time a Swansea side were victorious at Bramall Lane in the league.
The recent FA Cup success was memorable but the task of picking up a first win at this ground since the start of the last World War would have its rewards - a result agaist the Blades, or even a point, would take Brendan Rodgers' side up to second in the table.
And the early signs were convinving as Scott Sinclair showed his class to storm past three of his markers along the touchline, though that came to nothing, while Alan Tate's flick from a Mark Gower corner was easily held by Steve Simonsen in the Blades' goal.
Despite their lowly league position the home side enjoyed a small spell on top as Mark Yeates shot off target, Stephen Quinn saw his goal disallowed for offside and an Andy Reid free-kick was blocked by the Swans' wall.
But the best chance of the early exchanges fell to top-scorer Scott Sinclair with 20 minutes on the clock. He'd gone the last four games without scoring but when he latched on to Andrea Orlandi's through ball the wide man shrugged his marker but shot straight at Simonsen.
Ashley Williams also flashed a header wide from a corner which was one of few highlights of a quiet first-half.
But despite going through periods of time where both sides just didn't threaten it was the home side that drew first blood.
With two minutes left before the break the Swans threatened on the counter but as that was broken up the home side went route one to break the deadlock - Andy Reid picked out Ched Evans with his long pass and the Wales striker took his time before slotting underneath Dorus de Vries.
Sinclair tried to get his side back into the game in stoppage-time but he found the back of the Kop stand from 18-yards.
Half-Time: Blades 1 Swans 0
Rodgers made two changes for the start of the second period with Darren Pratley and Jermaine Easter sent on in place of Mark Gower and Craig Beattie respectively.
Within three minutes the visitors came close to levelling when Tate connected with Orlandi's corner but saw his header saved by Simonsen, and Arsenal loanee Kyle Bartley came to the Blades' rescue moments later as he blocked Easter's cross on the line after the latter was played through by Dyer.
The Swans continued to create the better chances and after Scott Sinclair saw his drive saved he turned provider to cross for Pratley but Simonsen also denied him with the header just after the hour. The goalkeeper came to their rescue again on 63 minutes when Sinclair cut in and fired straight at him.
David Cotterill went on as the Swans' last throw of the dice midway through the half, replacing Nathan Dyer, with booes echoing around the ground to welcome the one-time Blades player.
Time was ticking away for the visitors but they were gifted a chance quarter of an hour from the end when Easter dispossessed Nyron Nosworthy midway inside the United half, he picked out Sinclair but with the left foot shot high into the stand.
Ched Evans had a great chance to score his second three minutes from time but was denied by the legs of Dorus de Vries, but it didn't matter as they held on to record the win.