- Daniel Podence (45'+1')
Wolves boss Bruno Lage said he was still trying to integrate the club's new players into the side but was relieved to collect the first victory.
"We scored one goal and after that we were very brave in the way we defended," Lage said.
"We're very happy. I told the players it's one win, we have to build on it. We need to practice. The team that finished pre-season and the team we have now are so different.
"Players are arriving, we don't have time to train and have to put them straight into the games. We try our best to have our best strategy and they're performing well."
After the break Che Adams had the ball in the net for Southampton but it was ruled out for handball on a frustrating day for the forward.
Adams headed a Stuart Armstrong cross against the bar as Wolves held on for a win that moves them up to 14th on six points.
Southampton fall to 12th place with seven points from their opening six games and manager Ralph Hasenhuttl was frustrated at his side's failure to convert their opportunities.
"We had good chances to take something," Hasenhuttl said. "That we don't score today is normally not possible. Che knows it. He's frustrated because it must be a goal.
"It's 20 minutes to go and if we equalise, I would like to see what happens then."
- John Brooks
|Brighton & Hove Albion||13||6||4||3||+5||22|
|West Ham United||13||6||2||5||0||20|