Swansea were the better side in the first half, but when Wilfried Bony was shown a red card after 40 minutes, Southampton became the dominant team.
Here, Sports Mole takes a look at the 90 minutes and discusses the main talking points from the game.
On target: 2
On target: 4
Was the result fair?
If it wasn't for the red card, Swansea would have probably won. They were by far the better side in the first half, but the statistics tell the true story of the whole game. Southampton had almost all of the ball after the break and considering all their pressure, the winner was well deserved.
Swansea City's performance
If there was ever a 'game of two halves', this was it. Swansea were marvellous for 40 minutes. They attacked at pace, played brilliant, one-touch football, but just struggled to create many clear-cut chances. After the break, they hardly had a touch of the ball as they sat back and tried to hold on for a draw. They defended stoutly, but it became a little too much in the end. Bony aside, all the Swansea players can hold their heads high for their efforts today.
Koeman's side struggled in the first half, but the red card changed everything. In truth, for all their possession in the second period, they resorted to crosses towards Graziano Pelle on the whole. They eventually got the winner, but they should have created more against 10 men.
Sports Mole's man of the match
Ashley Williams: The Swansea captain continually intercepted Southampton passes in the first half, but his job was entirely different in the second. He made a few clearances and tackles, but it was his leadership qualities that really impressed as he cajoled his teammates throughout the game. He certainly didn't deserve to be on the losing side.
Bony's behaviour just cannot be excused. Yes, he was frustrated that he hasn't opened his account this term yet. And yes, he must have been annoyed that the ball got away from him on many occasions. But both challenges were so reckless, and his scissor tackle from behind on Maya Yoshida warranted a straight red card, let alone a second yellow. His two moments of stupidity cost Swansea the game today.
Jon Moss handled the game very well. He dished out many yellow cards in the first half and it looked in danger of escalating into a bloodbath as tackles flew in from either side. He had no option but to send Bony off and didn't get fazed by an incredibly irate home crowd.
Swansea City: After winning their first three games of the season, Swansea are in danger of losing three on the trot as they travel to Sunderland next Saturday.
Southampton: Depending on Chelsea's result tomorrow, Southampton could go to the top of the Premier League next week when they host QPR at St. Mary's Stadium.