Steve Jones gave Burnley an early lead, but their task was made all the harder with the 16th-minute dismissal of Wayne Thomas after clash wth John Viafara.
Two minutes later Grzegorz Rasiak headed a leveller, however the Clarets came back with a neat Andy Gray header.
The extra man told after the break when Inigo Idiakez fed Rudi Skacel and Chris Makin laid on the winner for Raziak.
Southampton manager George Burley
"I wasn't particularly happy with the way we played because we've played some good stuff of late.
"Burnely will feel disappointed. They deserved something, but to come away and score three, you've got to hope that's going to get you three points.
"You've got to look at the tremendous finishes and that's what won the game."
Burnley: Jensen, Duff, Thomas, McGreal, Harley, Elliott (Sinclair 27), James O'Connor, Hyde (Mahon 80), Jones (McCann 68), Gray, Noel-Williams.
Subs Not Used: Lafferty, Foster.
Sent Off: Thomas (16).
Goals: Jones 4, Gray 33.
Southampton: Davis, Wright, Baird, Pele, Makin, Belmadi (Dyer 78), Idiakez, Viafara, Skacel (Surman 84), Rasiak, Wright-Phillips (Jones 66).
Subs Not Used: Miller, Bale.
Goals: Rasiak 18, Skacel 54, Rasiak 73.
Ref: D Drysdale (Lincolnshire).