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.
Last season's leading goalscorer Bony had been named in the starting XI - restored 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.
Yoshida had come into the Southampton side for Toby Alderweireld, while James Ward-Prowse also replaced Steven Davis, and the Japan international twice bore the brunt of poor challenges from Bony.
The Ivorian needlessly bundled into Yoshida off the ball 20 minutes in before Bony's frustrations boiled over as he slid through the back of the defender after 39 minutes of a first half Swansea largely dominated.
Without Bony, 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.
That made 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, Swansea 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 - found space in the box to beat Fabianski.
