Leeds came from behind to take all three points for the second home game in a row, thanks to second half strikes from Bradley Johnson and Luciano Becchio.
Leeds United boss Simon Grayson made two changes from the side that won last time out at Watford.
Shane Higgs replaced the injured Kasper Schmeichel in goal and Max Gradel started in place of Lloyd Sam who was on the bench.
New signing Jason Brown who as been brought in as cover for Schmeichel was also on the bench whilst there was no place in the squad for fellow new signing Ramon Nunez.
Leeds started the game strongly and Becchio shot wide in the opening minutes.
Kilkenny was next to go close when he headed over from a Johnson cross.
After dominating in the first ten minutes, Leeds fell behind on thirteen minutes when Stephen Dobbie was put through after a long ball up front, which Naylor in the Leeds defence somehow managed to miss.
Swansea almost doubled the lead soon afterwards but this time Shane Higgs came to their rescue with a save from Scott Sinclair when he was through on goal.
The visitors were looking dangerous on the break and the speedy Nathan Dyer was causing problems for his old team mate Federico Bessone.
Higgs had to be alert again when a Dyer shot took a deflection of Naylor.
Leeds were still enjoying plenty of the ball but a solid Swansea defence was proving something of a barrier, Luciano Becchio was next to be denied when he saw his header blocked by defender Gary Monk.
Swansea continued to look a threat when breaking and Dobbie saw an effort excellently tipped round the post by Higgs.
Bradley Johnson nearly got the sides on level terms when his long-range effort hit the top of the bar with the keeper beaten.
Johnson`s chance was the final one of the half as Leeds went in one down at the break.
The visitors had the first chance of the second half when Scott Sinclair saw his shot go wide of the post.
Leeds equalised ten minutes into the second half when Bradley Johnson was on hand to rifle into the roof of the net after a ball into the middle by Max Gradel.
Simon Grayson quickly made his first substitution of the game when he brought on Lloyd Sam in place of Sanchez Watt.
The goal spurred Leeds into action and Gradel and Sam were causing Swansea problems.
Leeds took the lead just past the hour when after firstly, Sam and then Howson saw shots saved only for the ball to fall to Luciano Becchio who was on hand to score.
Things threatened to boil over minutes later when after a late challenge by Becchio on Swansea keeper De Vries; he retaliated by throwing the ball at Becchio.
The referee showed both players a yellow card when other officials could have quite easily have shown red to one or the other.
Gradel had Leeds next chance after good work from Kilkenny but his weak header didn`t trouble the Swansea keeper.
Swansea had strong appeals for a penalty turned down when Joe Allen was brought down in the area but the referee waved away the appeals.
Leeds made their second change of the afternoon inside the final fifteen minutes when Ross McCormack came on to replaced Neil Kilkenny and make his home debut.
McCormack had a very early chance to make a big impression on the Elland Road crowd but his free kick went over the bar.
Swansea had a good chance to equalise soon after when Van Der Gun who had just come on hit the side netting when in a good position.
Leeds made their final substitution of the afternoon with goalscorer Becchio replaced by Davide Somma with five minutes remaining.
Shane Higgs made a good save to deny Dobbie and from the follow up the striker shot over from a tight angle.
The fourth official put the board up to show five minutes of time added on as the visitors tried to get back on level terms.
Leeds came close to increasing their lead when De Vries tipped over a McCormack header.
Howson then had a chance for Leeds but his shot cleared the bar.
It was to be the last chance of the game as Leeds recorded their third win in a row in the Championship and move up to fifth in the table.
Higgs, Connolly, Naylor, Collins, Bessone, Howson, Kilkenny (McCormack 79), Johnson, Becchio (Somma 86), Watt (Sam 56), Gradel
Brown, Bruce, Clayton, Hughes,
De Vries, Tate, Williams, Monk, Taylor, Dyer (Van Der Gun), Gower, Orlandi (Allen 69), Sinclair, Cotterill, Dobbie
Cornell, Lopez, Serran, Thomas, Kuqi
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