Oli McBurnie scored his 11th goal of the season as the Swans moved to within six points of the play-offs following a 1-0 win over Sheffield United at the Liberty.
The Scottish striker tapped home in the 65th minute after being set up by Nathan Dyer, who had latched onto Mike van der Hoorn’s return pass into the box.
It proved a tight encounter in SA1, with not much between the sides, but McBurnie’s strike proved the difference as the Swans claimed a league double over the Blades.
The win moved the Swans onto 40 points from 28 games – six points adrift of sixth-placed Derby.
McBurnie returned from illness in the solitary change to the Swans starting line-up.
The striker missed the games at Aston Villa and Preston through sickness, with Courtney Baker-Richardson scoring in each of those fixtures in the absence of the Scotland international.
But McBurnie was fit enough to play a part in training during the week and he was restored to the XI.
Erwin Mulder retained his place in goal, with a back four of Kyle Naughton, Mike van der Hoorn, Joe Rodon and Connor Roberts ahead of him.
Matt Grimes and Leroy Fer were at the base of the midfield, with the trio of Nathan Dyer, Bersant Celina and Wayne Routledge playing in support of lone striker McBurnie.
Baker-Richardson dropped to the bench as Wilfried Bony missed out on a place in the matchday squad.
Sheffield United were unchanged from their win over QPR.
The opening chance didn’t come until the 22nd minute, and it took a fine save from Mulder to deny the visitors.
Enda Stevens’ fine cross was met by the boot of David McGoldrick, but Mulder got a toe to it to keep his goal in tact.
McGoldrick was again a threat as he met the cross of Mark Duffy, but he uncharacteristically flashed his header wide.
The visitors were on top and creating the better chances, and McGoldrick was again at the heart of things as his shot took a deflection off Cameron Carter-Vickers – on for the injured Rodon – and into the hands of Mulder.
That was it for the first half, with the Swans having to up their game after the break.
Graham Potter reacted by sending Daniel James on for Routledge for the second half.
The hosts had more intent in their play after the restart, and Grimes curled a 25-yard free-kick just over the crossbar.
Then McBurnie saw his shot blocked after some neat link up play involving himself, Celina and Dyer.
A minute later he was not to be denied.
Dyer ran at the defence and found van der Hoorn in the box, and the Dutch defender’s return pass sent the winger racing towards goal.
He brilliantly picked out McBurnie in a crowded box, and he stabbed home.
The goal gave the Swans an extra gear, and Dyer was denied in the box after Celina had sent James racing down the left flank.
James was involved again minutes later as Celina’s shot was parried into his path, and the Wales winger’s low drive was expertly kept out by keeper Dean Henderson.
After that it was a case of soaking up the Sheffield United pressure, and Potter’s men did just that to seal a hard-earned victory.
Swansea City: Erwin Mulder, Kyle Naughton, Mike van der Hoorn, Joe Rodon (Cameron Carter-Vickers, 21), Connor Roberts, Leroy Fer (captain), Matt Grimes, Nathan Dyer (Jay Fulton, 81), Bersant Celina, Wayne Routledge (Daniel James, ht), Oli McBurnie.
Subs: Kristoffer Nordfeldt, Barrie McKay, Jefferson Montero, Courtney Baker-Richardson.
Sheffield United: Dean Henderson, George Baldock, Enda Stevens, John Fleck (Gary Madine, 74), Jack O'Connell, Chris Basham, Billy Sharp (captain), John Egan, Oliver Norwood, David McGoldrick (Leon Clarke, 81), Mark Duffy (Kieran Dowell, 67).
Subs: Simon Moore, Paul Coutts, Richard Stearman, Marvin Johnson.