Nathan Dyer came agonisingly close to restoring parity before half time, but his shot hit the inside of the post before bouncing across the line and spinning out for a goal kick.
Southampton sealed all three points when a couple of defensive errors allowed Jay Rodriguez to fire the ball into the bottom corner in the 83rd minute.
Here, Sports Mole takes an in-depth look at an entertaining afternoon of football on the south coast.
On target 4
On target 7
Was the result fair?
In a word, no. All the statistics point towards a Swansea win being the fairest result but, in truth, a draw would have been the most fitting outcome of today's match. Overall, the first half was an even affair with both sides having their spells in control of the proceedings. However, the second 45 minutes were largely dictated by Swansea, as their 58% possession shows. Southampton's second goal came very much against the run of play and could give the impression that it was a comfortable win for the Saints, but it was anything but.
As has often been the case this season, it all comes down to defence. This afternoon saw Southampton keep their fifth clean sheet in their opening seven matches and, although Swansea enjoyed the lion's share of possession and overall were the better side, Southampton's defence simply would not budge. Apart from a small spell towards the start of the first half they were not a force to be reckoned with when going forward, but as it turns out they did not need to be. They did play some nice football at times but, overall, it was a disciplined and mature performance from the hosts.
Swansea will play worse than that this season and win. Michael Laudrup's side were really knocking on the door for the final hour or so of the match and their only problem was actually putting the ball in the back of the net. Dyer's shot that hit the post was a stroke of bad luck, but they created enough chances to get at least a point from this match, so it will be a frustrating defeat for the Swansea boss. Still, he would have seen plenty to make him happy this afternoon and, despite the result, will be pleased with his side's overall performance.
Sports Mole's man of the match
Artur Boruc: Had Swansea come away with a draw, or even a win, from this match, then Nathan Dyer would probably get this award. However, Artur Boruc's saves towards the end of the first half took on greater importance with each passing minute, and in the end he is probably more responsible for the win than any other Southampton player. Michu, Wilfried Bony and Jonjo Shelvey were all denied by the keeper as he kept yet another clean sheet. He was beaten on one occasion, but was lucky to see Dyer's shot come back off the inside of the post. Other than that, it was a top performance from the Southampton keeper.
This one has to go to the Swansea partnership of Jordi Amat and Chico Flores in central defence. Both players had a chance to deal with the danger in the 83rd minute, but neither took it upon themselves to successfully clear the ball, allowing Rodriguez in to score the killer goal. Up until that point it looked as if Swansea might grab an equaliser, but that goal sealed the win for the hosts and they have defensive errors from Amat and Chico to thank for that.
It was a mixed performance from Mike Dean. The first half was as easy a game as he is likely to officiate all season, but there were a number of talking points in the second period. The biggest was a disallowed goal for Southampton. Dean awarded the hosts a corner incorrectly but then, when they scored from that corner, ruled out the goal, also incorrectly. Once he had given the corner, the goal should have stood, but it was a curious case of two wrongs making a right for the referee and justice was, ultimately, done.
Southampton: Southampton will look to make it four league wins in a row when they face the daunting trip to Old Trafford to face Manchester United.
Swansea: Swansea will be hoping to regroup during the international period and they have a kind fixture awaiting them on their return as they face bottom side Sunderland at home.