Shefki Kuqi returned to haunt his old club Crystal Palace as the Swans sealed their first win at Selhurst Park in 90 years.
The striker marked his first start since arriving at the Liberty Stadium in January with his debut goal for the club after latching on to Andrea Orlandi's knock down with just 14 minutes gone.
The victory keeps the Swans in fifth place ahead of the visit of Newcastle on Saturday (12.45pm).
Palace: Julian Speroni; Nathaniel Clyne, Clint Hill, Johnny Ertl, Lee Hills; Shaun Derry (C), Neil Danns, Nick Carle (Sean Scannell, 81'), Danny Butterfield (Kieran Djilali, 58'), Darren Ambrose; Alan Lee (Calvin Andrew, 57').
Not Used: Stern John, James Comley, Alassane N'Diaye, Alex Wynter.
Swans:Dorus de Vries; Alan Tate, Garry Monk(C), Ashley Williams, Fede Bessone; Leon Britton (Gorka Pintado, 89'), Andrea Orlandi, Darren Pratley, Mark Gower (David Cotterill, 68'), Nathan Dyer (Joe Allen, 83'); Shefki Kuqi.
Not Used:David Cornell (GK), Lee Trundle, Tom Butler, Jazz Richards.
Attendance: 12,328 Away: 551
Referee: Mr. G Scott (Oxfordshire)
Shefki Kuqi was handed a first start against his former club at Selhurst Park.
The Finnish striker, who spent three years at Palace, came in for Gorka Pintado while two changes were also made in midfield.
Out went Joe Allen and Saturday's goalscorer David Cotterill and in came Andrea Orlandi and Mark Gower in their places.
The Swans were back in all white for this tricky fixture at Selhurst Park and had to deal with some early pressure from their hosts on a bitterly cold night in south London.
But Paulo's players rallied and with four minutes on the clock Andrea Orlandi forced the first effort on goal with a wicked half volley on four minutes, which was spilled but eventually gathered by Julian Speroni.
The Spaniard won his side a corner moments later which the ex-Barcelona youngster took but saw cleared, eventually landing at the feet of Nathan Dyer whose close effort drive was blocked inside the area.
It was a dominant start by the visiting side and on 14 minutes broke the deadlock to take a deserved lead - Garry Monk played the ball into the left-back position for Dyer to run on to, the winger hoofed the ball right-footed to the edge of the box where Orlandi flicked into Shefki Kuqi's path, the former Eagle controlling and steering the ball home from a tight angle.
The travelling contingent were in full voice and they were almost treated to a second four minutes later, Clint Hill having to clear a dangerous Mark Gower cross from inside his own six-yard area to concede a corner. Orlandi's delivery was cleared to the edge of the area where Nathan Dyer connected but sent his shot wide from 20-yards.
Palace hadn't offered anything inside the opening quarter of this game but with 20 minutes played Nick Carle was able to pull the trigger for Neil Warnock's side for the first time, his strike from just outside the box deflecting wide for the Eagles' first corner on the night.
The home started to enjoy a mini spell of dominance though had nothing to show for their efforts, while down at the other end the Palace defence had to put up with the physical presence of former colleague Kuqi, who was enjoying a fine start to his full debut.
Nathan Dyer fired into the side netting just before the half-hour and Nick Carle struck his side's first attempt on target moments, Dorus de Vries making an easy save.
Former Cardiff striker Alan Lee felt he should have been awarded a penalty when Kuqi appeared to put his hands onto his shoulders to clear a corner, the referee waved play on but the striker was on target with his first effort minutes later, a header straight at Dutchman de Vries.
Half-Time: Palace 0 Swans 1
The Swans made a bright start to this second-half and almost doubled their lead within five minutes of the re-start.
Alan Tate ploughed forward and on the edge of the box played a neat double one-two with Andrea Orlandi, the second pass through the legs of Shaun Derry but Orlandi's low drive was pushed around the post by Speroni.
But Palace weren't going to go down without a fight and shortly after coming on just before the hour substitutes Calvin Andrew and Kieran Djilali combined to almost snatch a leveller, the former crossing into the area and Djilali inches away from connecting.
Front-man Andrew had a chance of his own moments later but couldn't direct his shot on target.
Palace continued to pile on the pressure but it was Fede Bessone that came close to scoring next, turning his man and firing inchces wide of the targets.
Goalscorer Kuqi was forced to receive treatment in the middle of the park following a lunge by Shaun Derry, however the referee opted to play on, while Darren Ambrose came inches from levelling with 15 minutes to go.
The home side were awarded a free-kick 30-yards from goal and Johnny Ertl's delivery was flicked into the path of Ambrose at the back post, he did well to hook the ball back towards goal but pulled his effort across the face and just wide of the target.
Joe Allen and Gorka Pintado were thrown on for the closing stages of this fxture with the Swans having to deal with plenty of Palace pressure as they went seeking a late leveller but even after the five minutes of injury-time, fortunately, the Swans were able to hold on to record an important victory.