Darren Pratley's first-half double sent the Swans soaring up to fifth spot as they came away from Hillsborough with maximum points.
The midfielder broke the deadlock as early as the fifth minute with a cool finish from close-range before making it two shortly before the break, converting Nathan Dyer's cross from inside the six-yard box.
It was a first ever win away from home against Sheffield Wednesday, one that has handed boss Paulo Sousa an early Christmas present.
Craig Beattie missed out at Hillsborough with a knee injury and was replaced in attack by Gorka Pintado.
There was also a change in midfield where Jordi Lopez comes back into the side for Leon Britton while Tom Butler and Guillem Bauza were back on the bench following injury.
It was the first time that Spanish front-man Bauza has been involved with the first-team since August.
Owls: Lee Grant, Tommy Spurr, Lewis Buxton (Frank Simek, 54'), Darren Purse (C), Marcus Tudgay, Sean McAllister (Francis Jeffers, 46'), Darren Potter, Mark Beevers, James O'Connor, Leon Clarke, Jermaine Johnson (Luke Varney, 69').
Not Used: Richards Hinds, Etienne Esajas, Richard O'Donnell, Tom Soares.
Swans:Dorus de Vries; Angel Rangel, Ashley Williams, Alan Tate(C), Fede Bessone; Jordi Lopez (Albert Serran, 84'), Andrea Orlandi, Darren Pratley, Nathan Dyer (Tom Butler, 74'), Cedric van der Gun; Gorka Pintado (Guillem Bauza, 89').
Not Used:David Cornell (GK), Lee Trundle, Joe Allen, David Cotterill.
Attendance: 18,329 Away: 407
Referee: O Langford (West Midlands)
It was a bitterly cold afternoon in South Yorkshire when both sides trundled onto the Hillsborough surface for the final Championship clash before Christmas.
The band of Swans fans that braved the icy conditions in order to make the journey were given an early chance to cheer when Darren Pratley, racing onto Nathan Dyer's through ball, won his side a corner.
Andrea Orlandi's cross was cleared but Pratley was in with five minutes played to break the deadlock.
It was a move that started from the back - Dorus de Vries' clearance was flicked on by Cedric van der Gun to Gorka Pintado, the striker picked out the run of Pratley who glided into the area and finished cooly beyond Lee Grant to score his third of the season.
The visitors were handed another chance soon afterwards when Nathan Dyer was fouled in dangerous territory, but Jordi Lopez's delivery was cleared by the defence.
Wednesday rallied and so began a mini revival in front of goal - Jermaine Johnson cut inside to force an excellent save from de Vries on 13 minutes, forcing a corner, and from Darren Potter's delivery was met by the head of skipper Darren Purse and the Dutchman was called into action again, palming away for another corner.
The hosts continued to threaten but, having not scored in their previous five matchces, they just didn't look as if they were going to put the ball behind the sticks.
And despite not creating chances themselves, the Swans did find themselves two goals to the good on 36 minutes from only their second attempt at goal.
Orlandi used his magic to play the ball past Lewis Buxton to send Nathan Dyer to the byline, the winger crossed low to the near post where Darren Pratley was placed to instinctively place the ball past the 'keeper to find the bottom corner.
Half-Time: Owls 0 Swans 2
The snow that started to fall towards the end of the first-half had subsided by the time both sides were out for the second period, and within three minutes of the re-start they went searching for a third.
Andrea Orlandi was having a fine game in midfield and he came close to adding an assist to his portfolio of fine work on the day, picking out Pintado from a corner but the strikers effort was stopped by Grant.
Wednesday attempted an immediate comeback through Leon Clarke but his effort from outside the area was blocked by Swans skipper Alan Tate.
Gorka Pintado then went on to flick a harmless effort into safe hands of Grant before a lot of play was concentrated in the middle of the park.
The hosts' best chance of the early stages of the half fell just after the hour when a Darren Potter free-kick from the left of goal was collected by de Vries, after it was narrowly missed by Purse, while Jordi Lopez forced a save from the Owls' 'keeper when his strike from distance was pushed wide.
But Wednesday were desperately seeking a way back into this game, and 19 minutes from the end they came close through substitute Francis Jeffers.
Sean McAuley's side had everyone forward for Darren Purse's free-kick, the former Cardiff defender launched the ball into the area and it fell to Jeffers who struck but, fortunately, saw it deflect off the legs of Tate.
Paulo made his first change of the afternoon three minutes later as Tom Butler was introduced in place of Nathan Dyer, the Irishman's first appearance since going off injured at Peterborough earlier this month.
Wednesday continued to seek a way into this game but the home support were continuing to get frustrated as Dorus de Vries was not being tested by their players.
Albert Serran was brought on in place of Jordi Lopez to take up his position in front of the back four while fellow countryman Orlandi burst into the area moments later only to see the ball drift too far in front of him.
Francis Jeffers fired a shot wide in what was a frustrating afternoon for the hosts while Guillem Bauza made his return from injury with a run out for the final moments.