Southampton ground out a fourth straight win, after a valiant Victor Wanyama notched late on to see off ten-man Swansea.
Saints could consider themselves lucky not to be 1-0 down within the first twenty minutes, after Wayne Routledge's powerful effort cannoned off of Fraser Forster's crossbar.
Swansea continued to dominate and carved open a number of half-chances, before Wilfried Bony's glancing header from a Gylfi Sigurdsson corner was cleared off the line by Ryan Bertrand.
It looked as if Ki Sung-Yeung would convert after being gifted a clear sight at goal by Sigurdsson, but Saints skipper José Fonte was alert to the danger, blocking what looked like a goal-bound shot, with his body.
Despite having the better of the opening twenty-five minutes, with the better chances and looking far more threatening on the ball, Swansea were reduced to ten men after Wilfried Bony picked up a second yellow card for a reckless foul on Maya Yoshida.
The momentum of the game shifted. Where Southampton were previously glancing towards the scoreboard and counting down the minutes remaining until the half-time break, they now had the goal within their sights as they looked to find an opening.
The game was to remain tight and niggly, with few clear chances for either side. Tadić combined multiple times with his full-backs, Clyne and Bertrand, but Pellè was unable to convert the admittedly difficult chances that came his way.
First half bookings for central defensive pairing José Fonte and Maya Yoshida ensured that Koeman made a half-time switch, introducing Romanian defender Florin Gardos in the place of the Japanese international defender.
Ryan Bertrand soon became the third Saints player to go into the referee's book after a mistimed and clumsy challenge on former Southampton man Nathan Dyer, who was being watched by England manager Roy Hodgson.
A host of other English candidates were on show, with Forster, Clyne, Bertrand, Ward-Prowse, Cork, Shelvey, Routledge and Dyer all involved at the Liberty Stadium.
Repeated crosses from Tadić, Long, Clyne and Bertrand were confidently claimed by Fabianski throughout the afternoon, and it appeared that Saints would be unsuccessful to find a winner in south Wales.
The Saints had 70% of possession in the second half, but appeared unable to break the deadlock until a spell of bad luck ultimately brought good fortune to the visitors.
James Ward-Prowse fell to the ground, clutching his foot and signalling that he was unable to walk. After being stretchered off, Ronald Koeman sent on Victor Wanyama for the final quarter of an hour.
Little was Koeman, or anyone else in the stadium to know the significance of that particular change.
With time running out, Pellè fed the ball to Wanyama, who kept his balance and showed supreme strength to muscle past two Swansea defenders before slamming the ball into the top corner on the far side of the goal.
In the process, Wanyama became the first Kenyan to score in a Premier League game.
Netting for the first time in his Southampton career, Wanyama went with a muted celebration of simply standing and eye-balling the crowd and his team-mates. After the match, he admitted that he had not known how to celebrate the goal after waiting so long since his arrival from Celtic in the summer of 2013!
Swansea attempted to rejuvenate themselves, aided by the introduction of Marvin Emnes, but Saints managed to hold firm. In fact, it could have been two-nil, had Graziano Pellè or Steven Davis managed to keep their efforts down in the dying stages of the game.
This latest victory sees Saints rise to 2nd in the Barclays Premier League table, ahead of next week's hosting of Queens Park Rangers.