Ronald Koeman's new-look Saints moved up to second place in the Premier League table after the Kenya international's powerful late strike ended the hosts' resistance
The Kenya international prodded the ball home from inside the area with 10 minutes remaining as Swansea were left to rue Wilfried Bony's first-half dismissal.
Bony was restored to the starting XI as one of two changes that also included a full debut for Federico Fernandez, but while the striker's full-blooded approach initially posed Southampton problems, his enthusiasm got the better of him as he was shown two bookings before the break for fouls on Maya Yoshida.
The Japanese centre-back had come into the Saints side in place of Toby Alderweireld, while James Ward-Prowse also replaced Steven Davis, and the Japan international twice bore the brunt of poor challenges from Bony.
Without their topscorer from last season, Garry Monk's side were made to toil after the break and as Ronald Koeman's visitors piled the pressure on, Wanyama struck the crucial blow to make it three Premier League wins in a row for Southampton as Swansea followed up their defeat to Chelsea with another loss.
After a tentative start, the hosts could have taken the lead after 11 minutes when in-form Nathan Dyer almost connected with Wayne Routledge’s delivery from the left.
Bony initially failed to meet the ball as it flashed across the box before it also evaded Dyer – with England manager Roy Hodgson watching on from the stands.
Routledge then fired a swerving effort off target before Neil Taylor was required to go to ground to prevent Dusan Tadic from getting a shot away.
Bony was at the centre of things for Swansea as the game burst to life, his physical presence posing a problem for Southampton's backline and Yoshida in particular.
The Japanese was bundled over early on by Bony, which earned the former Vitesse striker his first yellow card.
Routledge then clipped the crossbar, following Gylfi Sigurdsson's well-timed throughball, before Graziano Pelle had Southampton's first effort on target just after the half-hour mark.
Ryan Bertrand denied Bony a first goal of the season, clearing the Ivorian's header off the line, before the striker's bustling approach cost him dearly six minutes before the break.
His aggressive tackle through the back of Yoshida earned him a second yellow card, giving Monk a half-time headache.
It was Koeman who opted for a half-time switch, however, replacing the cautioned Yoshida with Florin Gardos, and the Dutchman saw his side dominate possession for much of the second period.
Tadic had an effort deflected over the crossbar with Lukasz Fabianski helpless, before Pelle's header also found the roof of the net.
But just when Swansea appeared set for a hard-earned point, Wanyama - on in the 69th minute for Ward-Prowse - powered into the box before firing past Fabianski to claim all three points and take Southampton up to second in the table.