Bony scored from the spot after substitute Marvin Emnes had been brought down by Cheick Tiote to boost Swansea's survival hopes and condemn Newcastle to a fifth successive defeat.
Things looked bright for the hosts when Shola Ameobi gave them the lead midway through the first half, but Bony drew Swansea level on the stroke of half-time.
The game looked set to end all-square until Bony kept his cool from the spot to secure all three points for the Swans and move them up to 13th, six points clear of the drop zone.
After a slow start, the visitors from south Wales fashioned their first chance of the game on 18 minutes when Jonathan De Guzman fired over a dangerous cross from the right towards Bony, but Mike Williamson got to the ball first to deny the striker.
Newcastle suffered a blow on 20 minutes when Papiss Cisse was forced off with a knee injury he picked up earlier in the game, with Mathieu Debuchy coming on for the forward.
The Magpies broke the deadlock three minutes later as they finally ended their recent four-game goal drought with their first real attack of the contest.
Ameobi flicked on a long ball to Luuk De Jong and the Dutchman fed in Ameobi, who held off a couple of Swans challenges inside the box before slotting his left-footed shot past Michel Vorm for his first Premier League goal since December 2012 and Newcastle's first goal in over six hours of football.
Referee Chris Foy was also forced to leave the action just past the half hour due to injury, with fourth official Anthony Taylor taking over in the middle.
Newcastle suffered another injury problem on 38 minutes when De Jong was forced off with an ankle problem, with Loic Remy coming off the bench to replace him after missing the last six games through injury.
Swansea stunned Newcastle right on the stroke of half-time as they drew level when Bony rose highest above Williamson to head home Ben Davies' corner.
Newcastle started the second half brightly and Dan Gosling went close when his volley from Paul Dummett's cross was pushed wide for a corner by Vorm.
The home side created another opening on 56 minutes when Gosling got the better of Jonjo Shelvey down the right and he cut the ball back for Remy, who failed to direct his effort on target.
Newcastle continued to create the better of the openings in the second half and just past the hour mark, Vurnon Anita went close when he worked space on the edge of the box and flashed his left-footed shot just wide of the far post.
De Guzman had his Dutch compatriot Tim Krul scrambling in the Newcastle goal 12 minutes from time when his dipping shot from the edge of the box landed on the top of the net
Swansea had a great chance to grab the lead on 83 minutes when substitute Emnes played Bony in on goal, but Krul was quickly off his line to block the ball with his feet as the striker attempted to take the ball round the keeper.
The visitors grabbed all three points in the closing stages when Tiote brought down Emnes inside the box following a lightening counter attack and Bony scored from the spot to win it for Swansea.