Southampton manager Claude Puel achieved his first win in the Premier League
Though Southampton were dominant, the Saints struggled to exert their dominance on the scoreboard during the first half.
That all changed in the 64th minute when Charlie Austin - having earlier hit the crossbar with an effort - chested and shot to give his side the lead in what proved to be the match's only goal.
Puel's side manufactured 19 attempts on goal compared to Swansea's nine, and so they may be disappointed that they were not able to pull away from their opponents.
Here are two players who shone for Southampton, and one who may not enjoy re-watching the match in training on Monday.
Tadic played a large role in engineering Southampton's numerous attempts on goal.
His cross for Nathan Redmond in the first half should have seen the Saints finally break the deadlock, but Redmond's effort did not match the quality of Tadic's assist.
Austin though did not make the same mistake. Tadic whipped in an excellent ball to the far post - via a touch from Jordi Amat - with the 27-year-old striker finishing with aplomb as he controlled the ball with his chest and beat Swans 'keeper Lukasz Fabianski.
His passing was a joy to behold, and it's good to see Tadic receive attention for his football, rather than for having the ball ripped from his hands when wanting to take a penalty.
Austin and Tadic decide who will take the penalty as Virgil van Dijk intervenes
Austin only entered the fray in the 54th minute, but in his time on the field he posed as much of an attacking threat as any of the Saints' players.
Austin scores the game's only goal
His calm finish for the game's only goal was all the more impressive when compared with the profligacy of his teammates.
Fresh from two goals against Sparta Prague in the Europa League on Thursday, he wasted no time in making an impact, striking the crossbar within minutes of coming on before finally finding the back of the net.
Though Austin has found a purple patch, he is unlikely to start in Wednesday's EFL Cup tie with Crystal Palace due to his injury history.
As clinical as Austin's finish was, Redmond's finishing was not.
Twice in the first half, the 22-year-old striker was through on goal only to miss the target - initially firing wide, before firing over when he had been played through by Tadic's probing ball.
One cannot fault his confidence as Redmond attempted one shot from 25 yards out, only for it to end up alongside a spectator in the stands.
Redmond misses a chance to score
Redmond has only scored one goal in the Championship thus far this season, so he will need to up his scoring rate if he is to remain first-choice.
Have something to tell us about this article?