Substitute Nathan Dyer, a Mathieu Debuchy own goal and a spectacular Jonjo Shelvey strike gave the Swans just a second home win of the season.
Loic Remy had his header brilliantly saved by Michel Vorm for the visitors, but Newcastle were aggrieved after referee Howard Webb waved away penalty appeals for a Ben Davies handball and an Ashley Williams challenge on Yoan Gouffran in the second half.
With Michu and Wilfried Bony out, and no striker on the bench, the hosts moved midfielder Alejandro Pozuelo into an advanced role and were arguably the better for it as Newcastle struggled to handle their movement.
But, it was Dyer who gave them the lead.
Pozuelo drove down the left-hand side of the box and got in a cross that Tim Krul could only tip to the winger, who volleyed home.
Newcastle showed more attacking intent after the break and replays suggested they should have had a penalty in the 57th minute, when Remy's shot cannoned off a combination of Davies' chest and arm.
They were further frustrated when Gouffran tumbled as he and Williams contested a high ball and Swansea broke to clinch the win.
Pozuelo found Shelvey with a defence-splitting pass, the midfielder delayed his shot and Krul saved, only for the ball to rebound off Debuchy and into the net.
But former Liverpool man Shelvey, who a few minutes earlier had feinted to headbutt Debuchy during a heated stand-off, was not to be denied his goal, and curled home from 25 yards to seal the win.
During the opening half there was little to suggest Newcastle were a team brimming with confidence and good form as they simply stood off their hosts.
Swansea enjoyed plenty of possession but, as has often been the case this season, they created little, and it was the visitors who had the first big chance with their first genuine attack.
Yohan Cabaye whipped in a lovely cross to give Remy an unmarked header which Vorm did brilliantly to tip around his left-hand post.
Swansea continued to probe without much effect before losing Alvaro Vazquez to injury.
Dyer came on for him with Pozuelo being pushed forward and initially Swansea struggled to adjust to playing without a recognised frontman.
But Newcastle showed no inclination to take advantage, and were happy to sit and play on the counter.
Swansea were having almost three-quarters of possession, and Newcastle paid the price in time added on at the end of the first half when Dyer converted after Krul could only tip Pozuelo's cross straight to him.
It meant Swansea led at the interval at home for the first time this year, and they threatened to extend their lead as Krul gathered a Dyer header from a teasing De Guzman cross, before Shelvey whistled an effort just wide of the left-hand post.
Newcastle were at least starting to show positive signs and they felt they should have had a penalty in the 57th minute as Webb waved away their protestations that Davies had handled.
Debuchy then produced an awful tackle as Swansea looked to break, Webb produced a yellow, it could have been red.
Newcastle's pressing became more insistent, but left them vulnerable to the counter and Pablo Hernandez ought to have done better when freed by Dyer, with Mike Williamson making an excellent covering challenge as the Spaniard broke into the box.
But Swansea's lead did double moments later as Pozuelo's pass split the Newcastle defence and Debuchy diverted the ball into his own net.
But Newcastle were again frustrated as Webb had waved away appeals for a penalty after Gouffran went down seconds earlier.
Then Shelvey, after needlessly and petulantly moving his head towards Debuchy as they exchanged words a few minutes prior, completed the scoring.