Southampton stretched their unbeaten run to six games - five of those wins - as Saints' Irish striker Shane Long's header earned the spoils for his side.
Tight at the back and looking the more dangerous going forward compared to their Welsh opponents, Ronald Koeman will be happy with his team's classic away performance.
The result also means Fraser Forster has kept his sixth consecutive clean sheet since suffering a horrific knee injury in the previous season.
Long headed in the winning goal after meeting a perfect cross from James Ward-Prowse. This came from a flowing move which saw Steven Davis drive a perfect long-range pass to the on-rushing Cedric, who played the ball back to Ward-Prowse to hand Long's goal on a plate.
The Irishman's header was partially saved by Lukasz Fabiankski, but the Swansea City goalkeeper couldn't keep the ball from crossing the goal line.
Before Long's winner, Southampton had a perfectly good goal disallowed as Jose Fonte was adjudged to have fouled Fabiankski. Graziano Pelle had bundled the ball home from a corner but Fonte's supposed foul prevented Saints from taking the lead.
New Swans boss Francesco Guidolin hadn't tasted defeat in his three games since taking over at the club until today's defeat to in-form Saints.
While the scoreline was reflective of the match, Guidolin will be left disappointed as Swansea's late penalty shout was rejected by referee Stuart Moss. Saints defender Maya Yoshida looked like he had felled Alberto Paloschi in the dying minutes of the game.