Tom Butler's 25-yard strike sealed a first home league win of the season for nine-man Swansea City.
Lee Trundle put them ahead from the spot on 52 minutes after being fouled by Nick Montgomery.
United levelled 21 minutes later through Stephen Quinn's back-heel before Jordi Lopez saw red for Swansea.
Butler wrapped up the win eight minutes from time, but the Swans had to hold on after Nathan Dyer's second yellow reduced them to nine men.
It was a win the Swans desperately needed having failed in their last four attempts and not scored in the last three games.
But they were dealt an early blow when influential midfielder Ferrie Bodde lasted just eight minutes of his first start in 10 months after recovering from a cruciate knee ligament injury.
With the Swans already depleted in midfield before kick-off missing Leon Britton, Joe Allen and Darren Pratley, Wales defender Ashley Williams was handed a start in midfield.
It was not the ideal start against a Sheffield United side who had made a solid start to their Championship campaign losing just once in the league this season.
Bodde's exit along with the departure of United midfielder Keith Treacy were the only incidents of any note in a dour first half.
Stephen Quinn coolly brought Sheffield United level
But the match sprung to life on 52 minutes when Trundle, on loan from Bristol City, won himself a penalty after being brought down by Nick Montgomery.
The Liberty Stadium hero, who scored 86 goals in his previous four-year spell at the club, picked himself up to send Blades keeper Mark Bunn the wrong way.
United thought they had quickly got themselves level when Wales international Evans pounced after keeper Dorus de Vries parried David Cotterill's shot, but he was ruled offside.
They were level though on 73 minutes when James Harper's driven shot was put into the net by Quinn's back-heel.
And as the visitors pushed for a winner, they were boosted by the sending off of Lopez for a second booking.
But eight minutes from time, Butler grabbed the winner for Swansea out of nothing driving a low 25-yard shot into the back of the net - the first time they have scored more than one goal in a league game this season.
Paulo Sousa's side had to hang on in the closing stages though as they were reduced to nine men when Dyer picked up a second yellow card and the Blades piled on the pressure without success.
Interview: Swansea manager Paulo Sousa
Swansea manager Paulo Sousa:
"We did our job well with the spirit I want and with the character I want.
"We were playing against a very difficult team to beat and we need to be very proud.
"We have a lot of belief and confidence in the work we do."
Sheffield United manager Kevin Blackwell:
"We controlled the game but not the result. We gave away two sloppy goals and after that it was always hard to get a result.
"We started well but had to dig in a bit, although we went in at half-time full of confidence.
"We had a good goal disallowed but after equalising there was only one side in it.
"Two breakaways and credit to Swansea as they took the only two chances they had in the second half."
90:00+6:19 Booking Dorus De Vries is shown a yellow card for time wasting.
90:00+5:53 Shot from just outside the area by Matthew Kilgallon goes over the bar.
90:00+3:17 Sent off Red card for Nathan Dyer.
90:00+2:28 Thomas Butler takes a shot. Save by Mark Bunn. Mark Gower decides to take the corner short.
88:02 Unfair challenge on James Harper by Alan Tate results in a free kick. Glen Little crosses the ball in from the free kick, clearance made by Dorus De Vries.
86:19 Substitution Kyel Reid comes on in place of Andy Taylor.
83:51 Outswinging corner taken from the right by-line by Mark Gower.
83:01 Substitution Glen Little joins the action as a substitute, replacing Stephen Quinn.
81:54 Nathan Dyer provided the assist for the goal.
81:54 GOAL - Thomas Butler:Swansea 2 - 1 Sheff Utd Thomas Butler finds the back of the net with a goal from just outside the penalty box to the bottom right corner of the goal. Swansea 2-1 Sheff Utd.
80:08 Substitution Lee Trundle goes off and Ashley Richards comes on.
79:01 Ched Evans takes a shot. Ashley Williams gets a block in.
76:10 Sent off The referee sends off Jordi Lopez for second bookable offence.
75:49 Ched Evans fouled by Jordi Lopez, the ref awards a free kick. Free kick taken by Mark Bunn.
75:04 Jordi Lopez produces a right-footed shot from just outside the box that goes wide left of the goal.
72:40 Assist by James Harper.
72:40 GOAL - Stephen Quinn:Swansea 1 - 1 Sheff Utd Stephen Quinn finds the net with a goal from inside the six-yard box low into the middle of the goal. Swansea 1-1 Sheff Utd.
67:00 Unfair challenge on Kyle Walker by Jordi Lopez results in a free kick. Kyle Walker restarts play with the free kick.
66:01 Booking Jordi Lopez goes into the referee's book.
63:49 Free kick awarded for an unfair challenge on Lee Trundle by Nick Montgomery. Direct free kick taken by Alan Tate.
61:32 David Cotterill crosses the ball from the free kick right-footed from left channel, Jordi Lopez manages to make a clearance.
61:32 Booking Caution for Nathan Dyer.
61:17 Foul by Nathan Dyer on James Harper, free kick awarded.
60:38 Free kick awarded for an unfair challenge on Kyle Walker by Angel Rangel. Ched Evans takes the free kick.
58:48 Inswinging corner taken by David Cotterill.
58:31 David Cotterill takes a inswinging corner from the left by-line to the near post, clearance by Gorka Pintado.
57:32 Foul by Ched Evans on Mark Gower, free kick awarded. Angel Rangel restarts play with the free kick.
55:14 Substitution Federico Bessone goes off and Thomas Butler comes on.
51:34 GOAL - Lee Trundle:Swansea 1 - 0 Sheff Utd Penalty taken left-footed by Lee Trundle and scored. Swansea 1-0 Sheff Utd.
49:46 Penalty awarded for an unfair challenge on Lee Trundle by Nick Montgomery.
47:50 Free kick awarded for a foul by Lee Trundle on David Cotterill. Free kick taken by Ched Evans. Effort from outside the penalty box by Ched Evans goes wide left of the target.
45:17 David Cotterill gives away a free kick for an unfair challenge on Garry Monk. Garry Monk takes the direct free kick.
45:01 The second half has started.
Half Time
45:00+2:21 The referee calls an end to the first half.
45:00+1:10 Foul by Andy Taylor on Mark Gower, free kick awarded. Shot on goal comes in from Jordi Lopez from the free kick, Chris Morgan gets a block in. Outswinging corner taken from the right by-line by Mark Gower.
44:32 Unfair challenge on Garry Monk by Darius Henderson results in a free kick. Dorus De Vries takes the direct free kick.
41:37 Effort from the edge of the box by Jordi Lopez goes wide of the right-hand upright.
40:08 The referee blows for offside. Federico Bessone takes the free kick.
37:59 The assistant referee flags for offside against Gorka Pintado. Mark Bunn takes the indirect free kick.
36:34 Unfair challenge on Alan Tate by Stephen Quinn results in a free kick. Dorus De Vries takes the free kick.
34:58 Free kick awarded for an unfair challenge on Kyle Walker by Mark Gower. David Cotterill crosses the ball from the free kick right-footed from right wing. Unfair challenge on David Cotterill by Nathan Dyer results in a free kick. David Cotterill takes the direct free kick.
31:05 Mark Gower concedes a free kick for a foul on Darius Henderson. Kyle Walker takes the direct free kick.
28:51 Nathan Dyer takes a shot. Save made by Mark Bunn.
28:24 Foul by Darius Henderson on Jordi Lopez, free kick awarded. Alan Tate takes the free kick.
27:13 Substitution (Sheff Utd) makes a substitution, with Ched Evans coming on for Keith Treacy.
23:46 David Cotterill takes the outswinging corner, Chris Morgan takes a shot. Ashley Williams gets a block in.
20:13 Corner taken by Mark Gower, Garry Monk produces a header from inside the area that goes over the crossbar.
18:06 Free kick awarded for a foul by Federico Bessone on David Cotterill. David Cotterill crosses the ball from the free kick right-footed from right wing, clearance made by Mark Gower.
15:16 The referee blows for offside. Alan Tate takes the indirect free kick.
14:08 Darius Henderson challenges Jordi Lopez unfairly and gives away a free kick. Free kick taken by Dorus De Vries.
13:45 The assistant referee flags for offside against Gorka Pintado. Mark Bunn takes the free kick.
13:27 Free kick awarded for an unfair challenge on Alan Tate by Darius Henderson. Free kick taken by Alan Tate.
12:20 The referee gives a free kick against Stephen Quinn for handball. The ball is crossed by Jordi Lopez, Alan Tate takes a shot. Mark Bunn makes a save.
11:49 David Cotterill concedes a free kick for a foul on Jordi Lopez. Jordi Lopez takes the free kick.
10:10 Free kick awarded for a foul by Nick Montgomery on Gorka Pintado. Jordi Lopez crosses the ball in from the free kick, Chris Morgan manages to make a clearance. Corner taken by Mark Gower from the right by-line.
10:10 Booking Nick Montgomery goes into the book.
8:31 Inswinging corner taken right-footed by Keith Treacy, clearance by Garry Monk.
8:31 Substitution Lee Trundle on for Ferrie Bodde.
8:31 Corner taken right-footed by Keith Treacy from the right by-line to the near post, Garry Monk manages to make a clearance.
5:50 Corner from the left by-line taken by David Cotterill, Jordi Lopez manages to make a clearance.
5:16 Darius Henderson takes a shot from just outside the penalty area clears the crossbar.
1:27 Nick Montgomery fouled by Jordi Lopez, the ref awards a free kick. Free kick taken by Kyle Walker.
0:00 The ref blows the whistle to start the match.
Live text and data provided by The Press Association.
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