Michu broke the deadlock for the Swans in the 58th minute with a header from Pablo Hernandez's cross as Tim Krul was punished for a poor clearance.
Jonathan de Guzman turned home a second from close range three minutes from time after Krul could only parry Danny Graham's shot.
Newcastle pulled a goal back thanks to Demba Ba's header just before the final whistle but there was not enough time to find an equaliser.
It had been a frustrating afternoon for the Magpies even before kick-off, with Papiss Cisse not allowed to play after Senegal invoked FIFA's five-day rule after he missed an international appearance in midweek.
It was nevertheless an exciting and open game from the very start as Newcastle desperately tried to put on a show for their supporters and Swansea threatened on the counter-attack, with both goalkeepers called into action in the first half.
Krul produced a fine stop to keep out Michu's shot from distance after a quarter of an hour, while he then did well to stand up tall and narrow the angle on Itay Shechter after a hopeful long ball had caught out Mike Williamson.
At the other end, Hatem Ben Arfa was by far the greatest threat and, after striking one effort into the side-netting from a tight angle, he made Gerhard Tremmel dive to his right to pull off an acrobatic save.
Newcastle stepped up the pressure at the start of the second half as Shola Ameobi came on to replace Shane Ferguson and Sammy Ameobi got into the game more down the left, but Ba squandered a couple of good opportunities and the hosts were made to pay when Michu opened the scoring.
Ba then headed a 64th-minute Cheick Tiote cross towards goal, but without the power to trouble Tremmel, and the keeper then got a good block on Shola Ameobi's cross after a dazzling run from deep by Ben Arfa.
The Magpies were demonstrating little composure in front of goal, and were grateful to see Michu uncharacteristically do the same to miscue Hernandez's 76th-minute cross wide.
But the sting in the tail arrived three minutes from time when Krul could only parry substitute Graham's shot and De Guzman smashed home the rebound from a tight angle, making Ba's late header after substitute Sylvain Marveaux had struck the bar practically irrelevant.