Victor Wanyama's first Southampton goal finally ended the resistance of 10-man Swansea in Saturday's Barclays Premier League clash at the Liberty Stadium.
Wanyama struck with an excellent angled finish just as Swansea - who had Wilfried Bony sent off six minutes before half-time for two bookable offences - looked like withstanding intense Saints second-half pressure.
Bony saw red for the first time in English football after felling Saints defender Maya Yoshida with a needless tackle from behind on the halfway line.
The Ivorian had already been booked for catching Jose Fonte in mid-air after 20 minutes, and, while that decision might have been slightly harsh with the striker's focus firmly on the ball, there was no disputing the second caution.
Swansea had dominated proceedings until Bony's dismissal, but the red card proved the game's turning point as Southampton took total command in the second period.
They had to wait until the 80th minute for their winner, though, when Graziano Pelle fed Wanyama and his unerring finish gave Southampton their third consecutive victory and moved them above Swansea in the table.
Roy Hodgson was visiting the Liberty Stadium for the first time in his capacity as England manager and there were two fascinating battles on the flanks for him to assess.
Nathan Dyer was up against Ryan Bertrand and Nathaniel Clyne was marking Wayne Routledge, and the Swansea wingers enjoyed early success.
Routledge sent over an excellent 12th-minute cross but Dyer was unable to make a proper connection and Bertrand cleared the danger.
Swansea were calling the shots in the early stages and Gylfi Sigurdsson fired straight at Fraser Forster in the Saints goal before Routledge sent an ambitious volley wide.
The temperature levels rose as Bony and Fonte picked up bookings for fouls on each other and Yoshida was also cautioned for dissent after Dyer clattered into Shane Long.
Swansea almost took a 28th-minute lead when Sigurdsson slipped through Routledge and the winger, choosing to shoot with the outside of his right foot, struck the top of the crossbar.
Southampton had not offered much in attack but a free-flowing move involving Dusan Tadic and Bertrand ended with Pelle scuffing a shot which Lukasz Fabianski comfortably collected at his near post.
But Saints were fortunate to survive when Bony met Sigurdsson's corner and Bertrand was in the right place to clear off the line. It was Bony's last positive involvement as he soon saw red.
Southampton inevitably dominated the second period, both in terms of possession and territory, as Swansea left Sigurdsson up front on his own and retreated deeper and deeper towards their own goal.
Tadic's deflected drive ended up on the roof of the Swansea net and Clyne crossed for Pelle to send a header straight at Fabianski on his goal-line.
The Serbian was really starting to pose problems down Swansea's right and his cross found the head of Pelle, whose header forced Fabianski to tip over.
Pelle had an even better opportunity when substitute Steven Davis picked him out. The unmarked Italian headed wide from 10 yards, but the striker redeemed himself when he sent Wanyama through for the decisive goal 10 minutes from time.