Two strikes from Jonathan de Guzman and Ben Davies's first goal saw Swansea secure a comprehensive win over Stoke.
After a goalless first half Davies broke the deadlock when he fired a low shot past Asmir Begovic.
De Guzman doubled the lead with a curling free-kick before completing a fine Swans move with an accomplished finish to make it three.
Michael Owen's late header, his first goal for Stoke, was a mere consolation for the visitors.
'Dominant' Swansea delight Laudrup
Stoke offered very little but the win will give Swansea confidence for their Capital One Cup semi-final second leg against Chelsea on Wednesday.
The Swans made a probing start to the game with Michu firing high and wide after being teed up by Itay Shechter, who capitalised on a mistake by Robert Huth.
Stoke found it hard to break out of their own half during the early exchanges but gradually improved.
Despite their promising start the home side did not trouble Asmir Begovic, with Ki's long-range effort clearing the crossbar.
In reply Peter Crouch, making his first league start since November, volleyed over the bar.
Matthew Etherington found himself in the area after playing a neat one-two with Charlie Adam but the winger fired into the side-netting.
The previous three Premier League meetings between the sides had ended in 2-0 home victories, including Stoke's win at the Britannia Stadium in September.
Swansea upped their game as Pablo Hernandez and Davies saw efforts deflected, and Ki turned an effort wide of the post.
The best move of what had been a forgettable first half saw Michu head wide from six yards following Angel Rangel's neat cross from the right. And De Guzman missed another excellent opportunity when he fluffed his shot after Wayne Routledge's cross found him in a packed penalty area.
De Guzman again had his sights on goal early in the second half but the Dutchman blazed his effort over the bar.
But two minutes later Swansea finally broke the deadlock courtesy of a first senior goal for 19-year-old full-back Davies.
The Wales international showed strength and composure as he beat two players before coolly slotting the ball past Begovic.
Michael Laudrup's side were now fully in control and when Michu was brought down on the edge of the area by Adam, De Guzman curled the free-kick into the net, beyond a stranded Begovic.
Pulis praises 'fantastic' Swansea
New Swans loan signing Roland Lamah was introduced as a replacement for Hernandez while Stoke's Kenwyne Jones, a possible Swansea target, replaced Crouch.
Another substitute, Cameron Jerome missed a golden chance to reduce the deficit when he put the ball over from a yard out.
The hosts completed the win when De Guzman finished off a sweeping move with an accomplished finish 10 minutes from time after receiving a pass from Danny Graham.
Owen scored with a header from six yards for his first goal in Stoke colours but it was too late to prevent the Swans moving four points clear of their visitors and into eighth place in the Premier League.
Swansea City manager Michael Laudrup:
"We dominated from the first minute. In the first half Stoke had to defend very deep and the only bad point was we did not score from the two or three good chances we had.
"In the second half we continued, but I knew we needed something special to score the first goal. If we scored the first goal I was sure we would win."
Stoke City manager Tony Pulis:
"We were second best from the first whistle to the last. Swansea were better and deserved to win. I've got no excuses.
"You have good and bad days in football and this was a bad day for us. We looked a yard short all over the pitch. We looked sluggish and sloppy.
"Whether it's the fact we played [Crystal] Palace in extra-time [in the FA Cup] and had to travel down early and had not been able to do anything for two days because of the snow, I don't know. But it wasn't us today."
Inswinging corner taken from the left by-line by Glenn Whelan.
The assist for the goal came from Cameron Jerome.
90:00 +0:54 Goal scored
Goal! - Michael Owen - Swansea 3 - 1 Stoke Michael Owen finds the net with a headed goal from inside the six-yard box. Swansea 3-1 Stoke.
Glenn Whelan takes a outswinging corner.
The ball is swung over by Geoff Cameron, save by Michel Vorm.
Corner from the left by-line taken by Glenn Whelan, Headed effort on goal by Ryan Shawcross from inside the penalty box misses to the right of the target.
Cameron Jerome concedes a free kick for a foul on Angel Rangel. Michel Vorm takes the direct free kick.
Substitution Michael Owen replaces Matthew Etherington.
Effort on goal by Robert Huth from long range goes harmlessly over the bar.
Sung-Yeung Ki gives away a free kick for an unfair challenge on Jonathan Walters. Direct free kick taken by Glenn Whelan.
Handball decision goes against Glenn Whelan. Garry Monk takes the indirect free kick.
Assist on the goal came from Danny Graham.
79:29 Goal scored
Goal! - Jonathan de Guzman - Swansea 3 - 0 Stoke Jonathan de Guzman scores a goal from inside the penalty box to the bottom left corner of the goal. Swansea 3-0 Stoke.
Unfair challenge on Roland Lamah by Geoff Cameron results in a free kick. Free kick crossed right-footed by Jonathan de Guzman, blocked by Robert Huth. Corner taken by Wayne Routledge, clearance made by Jonathan Walters.
Substitution Leon Britton comes on in place of Miguel Michu.
Substitution Danny Graham is brought on as a substitute for Itay Shechter.
Cameron Jerome takes a shot from close in clearing the crossbar.
Unfair challenge on Jonathan Walters by Roland Lamah results in a free kick. Glenn Whelan crosses the ball from the free kick right-footed from right wing, Miguel Michu manages to make a clearance.
Unfair challenge on Dean Whitehead by Ben Davies results in a free kick. Free kick crossed right-footed by Glenn Whelan, Michel Vorm makes a save.
The ball is crossed by Matthew Etherington, Michel Vorm makes a save.
Itay Shechter gives away a free kick for an unfair challenge on Steven Nzonzi. Robert Huth takes the direct free kick.
Kenwyne Jones gives away a free kick for an unfair challenge on Ben Davies. Free kick taken by Michel Vorm.
Substitution Pablo Hernandez leaves the field to be replaced by Roland Lamah.
Substitution Cameron Jerome on for Charlie Adam.
Substitution Kenwyne Jones comes on in place of Peter Crouch.
Inswinging corner taken from the right by-line by Matthew Etherington, Ben Davies manages to make a clearance.
Inswinging corner taken by Glenn Whelan from the left by-line, clearance made by Miguel Michu.
The ball is sent over by Dean Whitehead, Garry Monk manages to make a clearance.
Assist on the goal came from Miguel Michu.
56:18 Goal scored
Goal! - Jonathan de Guzman - Swansea 2 - 0 Stoke Jonathan de Guzman hits the back of the net with a goal direct from the free kick from just outside the penalty area to the top left corner of the goal. Swansea 2-0 Stoke.
Free kick awarded for a foul by Charlie Adam on Miguel Michu.
Ashley Williams fouled by Peter Crouch, the ref awards a free kick. Garry Monk takes the free kick.
Geoff Cameron sends in a cross, Wayne Routledge manages to make a clearance.
Miguel Michu takes a shot. Ryan Shawcross gets a block in.
Assist by Sung-Yeung Ki.
48:14 Goal scored
Goal! - Ben Davies - Swansea 1 - 0 Stoke Goal scored by Ben Davies from just inside the area to the bottom right corner of the goal. Swansea 1-0 Stoke.
Jonathan de Guzman takes a shot from just outside the penalty area clears the crossbar.
The ball is swung over by Angel Rangel, Robert Huth manages to make a clearance.
Robert Huth fouled by Itay Shechter, the ref awards a free kick. Free kick taken by Glenn Whelan.
The referee starts the second half.
45:00 +0:14 Half time
Half Time The first half comes to an end.
Matthew Etherington takes a shot. Save by Michel Vorm. Inswinging corner taken right-footed by Jonathan de Guzman, save by Asmir Begovic.
Corner taken by Jonathan de Guzman played to the near post, Ryan Shawcross makes a clearance.
The ball is swung over by Geoff Cameron, clearance by Garry Monk.
Wayne Routledge sends in a cross.
Corner taken right-footed by Jonathan de Guzman.
Angel Rangel delivers the ball, Robert Huth manages to make a clearance.
The ball is sent over by Angel Rangel, Headed effort from inside the penalty area by Miguel Michu misses to the right of the target.
Peter Crouch gives away a free kick for an unfair challenge on Garry Monk. Free kick taken by Garry Monk.
Ben Davies takes a shot. Robert Huth gets a block in. Pablo Hernandez takes a outswinging corner from the right by-line to the near post, Sung-Yeung Ki produces a right-footed shot from deep inside the six-yard box which goes wide of the right-hand post.
Jonathan de Guzman takes a outswinging corner to the near post, Glenn Whelan manages to make a clearance. Pablo Hernandez takes a shot. Dean Whitehead makes a clearance. Short corner taken by Jonathan de Guzman from the left by-line.
Matthew Etherington produces a left-footed shot from deep inside the six-yard box which goes wide of the left-hand post.
The ball is swung over by Dean Whitehead, Garry Monk makes a clearance.
Wayne Routledge sends in a cross.
Pablo Hernandez concedes a free kick for a foul on Geoff Cameron. Robert Huth takes the direct free kick.
Effort on goal by Peter Crouch from just inside the penalty area goes harmlessly over the target.
Miguel Michu takes a shot. Asmir Begovic makes a save. Jonathan de Guzman concedes a free kick for a foul on Charlie Adam. Asmir Begovic restarts play with the free kick.
Angel Rangel produces a cross, clearance made by Robert Huth.
Peter Crouch challenges Garry Monk unfairly and gives away a free kick. Michel Vorm takes the free kick.
The assistant referee signals for offside against Itay Shechter. Asmir Begovic takes the indirect free kick.
Free kick awarded for a foul by Wayne Routledge on Dean Whitehead. Free kick taken by Asmir Begovic.
Inswinging corner taken right-footed by Glenn Whelan played to the near post, Angel Rangel manages to make a clearance.
Effort on goal by Sung-Yeung Ki from outside the box goes harmlessly over the bar.
Free kick awarded for an unfair challenge on Ryan Shawcross by Miguel Michu. Asmir Begovic takes the direct free kick.
Free kick awarded for a foul by Geoff Cameron on Itay Shechter. Angel Rangel restarts play with the free kick.
Jonathan de Guzman concedes a free kick for a foul on Charlie Adam. Matthew Etherington takes the direct free kick.
Ben Davies sends in a cross.
Peter Crouch fouled by Angel Rangel, the ref awards a free kick. Geoff Cameron takes the free kick.
Foul by Geoff Cameron on Angel Rangel, free kick awarded. Free kick crossed by Jonathan de Guzman, clearance by Glenn Whelan.
Miguel Michu produces a left-footed shot from just outside the penalty area that goes harmlessly over the target.
The referee blows for offside. Free kick taken by Asmir Begovic.
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