Javier Hernandez's early strike ensured Manchester United kept up the pressure on league leaders Manchester City.
Angel Rangel's error allowed Ryan Giggs to cross for Hernandez, who tapped in after 11 minutes.
United went on to control the first half but Scott Sinclair wasted an excellent chance for the home side, miscuing a shot in the 22nd minute.
Swansea briefly threatened after the break before Phil Jones hit a post late on as United closed the game out.
But this was far from a vintage United performance as they once again struggled to find cohesion in the final third.
Swansea penetrated well down the flanks, with Nathan Dyer giving Patrice Evra a particularly uncomfortable match before the Frenchman was substituted early in the second half after collecting a yellow card.
But the killer edge belonged to United, and more specifically Hernandez as the striker again showed his appetite for away goals by scoring his 13th away from Old Trafford.
United needed an immediate response after rivals Manchester City earlier opened up an eight-point lead at the top of the table, and 11 minutes was all it took to stamp their authority at the Liberty Stadium.
Swansea's passing philosophy has won plaudits in their debut Premier League season, but their willingness to pass in all areas proved to be their downfall.
Giggs intercepted Rangel's weak square pass on the edge of Swansea's penalty area, and the Welshman's precise low cross to Hernandez allowed the Mexican to stab home his fifth goal of the season.
DID YOU KNOW?
- This was Manchester United's first win at Swansea after two draws and six defeats
But the lead should have been cancelled out 10 minutes later when Sinclair was guilty of a horrendous miss.
Wayne Routledge, starting in midfield as Joe Allen's slight knock relegated him to the bench, delivered a perfect far-post cross but Sinclair fluffed his shot from six yards and United cleared.
Giggs and Michael Carrick, making his first Premier League start this season, began to control midfield, benefiting from far too much time and space, but Evra's low drive was all that troubled Michel Vorm in the Swansea goal before the interval.
United's unchallenged dominance in midfield had obviously caught Brendan Rodgers's eye as the Swansea manager's response was to replace Routledge with Allen for the second half.
And the young Welshman was immediately involved as he set up Sinclair, whose shot forced David de Gea to save at his near post.
United broke with trademark fluidity from the resulting corner but poor control from Hernandez cost him the chance to double the lead.
Swansea, who had never lost in their eight previous meetings with United at home, showed greater urgency after the break, and the visitors were indebted to Vidic's tenacity in the air to clear twice in his own six-yard box.
Carrick's despairing lunge then blocked Danny Graham's goalbound effort as the home side's pressure grew in the final 20 minutes.
United's only second-half attempts on target were two speculative long-range Rooney efforts until a semblance of control returned to their play in the final 10 minutes.
Another slick counter-attack freed Phil Jones down the right, but his low effort across the face of goal clipped the far post after the slightest of touches from Vorm.
That move was the closest United came to reaching anywhere near top gear, but they did enough to end Swansea's unbeaten home record this season as they closed out for a victory that takes them back to within five points of Premier League pacesetters City.
Swansea manager Brendan Rodgers: "Our squad is very thin but you could see the confidence in the team in the second half.
"In the first half we were nowhere near our level and we made it too comfortable for Manchester United. In the end we're disappointed not to get a point.
"But there's a great confidence in the team and if we carry on this season like we played in the second half then we'll give ourselves a chance."
Manchester United manager Sir Alex Ferguson: "We didn't really look as though we were going to lose a goal.
"In the past when we have won titles we have won four or five games 1-0. Michael Carrick was fantastic and we spoke to Phil Jones this morning about how he felt after the busy week he has had.
"But he wanted to play and that's not a surprise because he's got a lot of energy. He was magnificent in the second half."
- 01 Vorm
- 02 Williams
- 03 Taylor
- 16 Monk
- 22 Rangel
- 07 Britton
- 11 Sinclair
- 12 Dyer
- 15 Routledge (Allen - 46' )
- 27 Gower (Dobbie - 79' )
- 10 Graham
- 25 Tremmel
- 44 Moras
- 24 Allen
- 29 Richards
- 14 Dobbie
- 18 Lita
- 19 Moore
- 01 De Gea
- 03 Evra Booked (F Da Silva - 51' )
- 04 Jones
- 05 Ferdinand
- 15 Vidic
- 11 Giggs (Fletcher - 76' )
- 13 Park Ji-sung
- 16 Carrick
- 17 Nani
- 10 Rooney
- 14 Hernandez (Valencia - 84' )
- 34 Lindegaard
- 06 Evans
- 20 F Da Silva
- 18 Young
- 24 Fletcher
- 25 Valencia
- 09 Berbatov
Live Text Commentary
Full Time The final whistle is blown by the referee.90:00 +3:02
Effort from the edge of the area by Luis Nani goes wide of the right-hand post.90:00 +0:47
Free kick awarded for a foul by Angel Rangel on Fabio Da Silva. Free kick taken by Rio Ferdinand.89:32
Phil Jones takes a shot from inside the six-yard box that strikes the post.88:36
Wayne Rooney takes a shot from inside the six-yard box clearing the crossbar.88:03
Wayne Rooney takes a shot. Ashley Williams gets a block in.87:17
Luis Nani takes a outswinging corner to the near post, Garry Monk manages to make a clearance. Corner taken by Luis Nani, save by Michel Vorm.85:52
Luis Nani takes a shot. Garry Monk gets a block in.83:14 Substitution
Substitution Antonio Valencia replaces Javier Hernandez.79:24
Danny Graham is ruled offside. Rio Ferdinand restarts play with the free kick.78:28 Substitution
Substitution Stephen Dobbie is brought on as a substitute for Mark Gower.76:45
The offside flag is raised against Javier Hernandez. Indirect free kick taken by Michel Vorm.75:13 Substitution
Substitution Darren Fletcher comes on in place of Ryan Giggs.72:15
Danny Graham takes a shot. Blocked by Rio Ferdinand. Ashley Williams takes a shot. Nemanja Vidic gets a block in.71:16
Fabio Da Silva gives away a free kick for an unfair challenge on Mark Gower. Mark Gower crosses the ball in from the free kick.69:53
Wayne Rooney takes a shot. Save by Michel Vorm.66:47
Outswinging corner taken by Mark Gower from the right by-line played to the near post, Ryan Giggs makes a clearance.65:36
Nathan Dyer concedes a free kick for a foul on Fabio Da Silva. Free kick taken by David De Gea.63:24
Wayne Rooney takes a shot. Save by Michel Vorm.62:48
Nathan Dyer fouled by Fabio Da Silva, the ref awards a free kick. Garry Monk restarts play with the free kick.
Leon Britton fouled by Wayne Rooney, the ref awards a free kick. Ashley Williams restarts play with the free kick.59:23
Mark Gower gives away a free kick for an unfair challenge on Ji-Sung Park. Michael Carrick takes the free kick.57:38
Free kick awarded for a foul by Wayne Rooney on Michel Vorm. Michel Vorm takes the direct free kick.54:46
Corner taken by Mark Gower from the left by-line, Garry Monk takes a shot. Blocked by Rio Ferdinand. Mark Gower takes a corner.52:53
Garry Monk concedes a free kick for a foul on Javier Hernandez. Ryan Giggs takes the direct free kick.50:30 Substitution
Substitution Fabio Da Silva comes on in place of Patrice Evra.48:17
Scott Sinclair takes a shot. Save made by David De Gea. Corner taken by Mark Gower from the right by-line.47:42
The referee blows for offside. Michel Vorm takes the direct free kick.46:29
Free kick taken by Angel Rangel.46:29 Booking
Booking Booking for Patrice Evra for unsporting behaviour.46:13
Unfair challenge on Nathan Dyer by Patrice Evra results in a free kick.45:01
The match restarts for the second half.45:01 Substitution
Substitution Joe Allen replaces Wayne Routledge.45:00 +1:06 Half time
Half Time The players leave the pitch at half time.44:00
Michael Carrick concedes a free kick for a foul on Nathan Dyer. Direct free kick taken by Mark Gower.41:48
Scott Sinclair takes a shot. Nemanja Vidic gets a block in.40:33
Unfair challenge on Leon Britton by Luis Nani results in a free kick. Neil Taylor takes the direct free kick.39:24
Shot from just outside the area by Luis Nani misses to the left of the target.37:54
Free kick awarded for an unfair challenge on Mark Gower by Ryan Giggs. Free kick taken by Neil Taylor.36:57
Inswinging corner taken right-footed by Mark Gower from the left by-line to the near post, Michael Carrick manages to make a clearance.36:30
Wayne Rooney produces a right-footed shot from 35 yards and missed to the left of the goal.34:28
Free kick awarded for an unfair challenge on Javier Hernandez by Garry Monk. Ryan Giggs fires a strike on goal direct from the free kick.26:27
Wayne Rooney takes a shot. Ashley Williams gets a block in.24:07
Effort from outside the box by Neil Taylor goes wide right of the target.22:07
Wayne Routledge takes a shot. Blocked by Rio Ferdinand.21:09
The referee blows for offside. Free kick taken by Michel Vorm.19:49
Patrice Evra takes a shot. Save made by Michel Vorm.15:20
Free kick awarded for an unfair challenge on Mark Gower by Luis Nani. Free kick taken by Leon Britton. Inswinging corner taken by Mark Gower, save made by David De Gea.12:41
Scott Sinclair produces a right-footed shot from long range which goes wide right of the goal.10:04
The assist for the goal came from Ryan Giggs.10:04 Goal scored
Goal! - Javier Hernandez - Swansea 0 - 1 Man Utd Javier Hernandez finds the back of the net with a goal from close range low into the middle of the goal. Swansea 0-1 Man Utd.4:11
Javier Hernandez fouled by Garry Monk, the ref awards a free kick. Phil Jones takes the free kick.3:00
Mark Gower has an effort at goal from just outside the penalty box which goes wide of the left-hand post.0:00
The referee starts the match.
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