Darren Pratley's two goals condemned Sean McAuley to a losing start as Sheffield Wednesday caretaker boss.
The midfielder took just five minutes to put Swansea in charge, Gorka Pintado laying the ball on for Pratley to take in his stride and beat Lee Grant.
Wednesday rallied and it took a good save from Dorus de Vries to keep out Jermaine Johnson's fierce shot.
But the Owls then struggled and Pratley struck a second goal, meeting Nathan Dyer's low cross at the near post.
Wednesday parted company with Brian Laws last weekend but McAuley was unable to inspire an improvement as Swansea maintained their push for promotion.
The Owls are now winless in the last 10, having lost the last six and face the harsh reality of relegation if they do not make drastic improvements.
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QPR 1 - 1 Sheff Utd
New Queens Park Rangers manager Paul Hart saw his side draw with Sheffield United in his first game in charge.
Mikele Leigertwood opened the scoring for the home side with a right-footed strike from the edge of the area after just two minutes.
Toni Kallio set up Richard Cresswell to fire home from close range for the equaliser six minutes later.
Ben Watson headed against the crossbar in injury-time for the home side but both teams had to settle for a point.
QPR manager Paul Hart:
"I thought we played extremely well. In the second half we were excellent, it was wave after wave.
"I work with players to try to help them improve. I'm here to steady the ship.
"I think this is a great club and it's a privilege to be working here."
Sheffield United manager Kevin Blackwell:
"We talked about it in the week, it's not the time to be playing a team when a new manager walks through the door.
"The players have got to show them what we are about.
"All the talk was about QPR but my players were very resilient and did a professional job."
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