For only the second time this season Sean Dyche's side finished without a point after scoring the first goal of the game.
Burnley - who were beaten 4-2 by Leicester City after Chris Wood had opened the scoring at the King Power Stadium in September - had been cruising on the south coast.
The New Zealander struck first against the Saints when beating Fraser Forster from the spot in the 12th minute.
And the visitors extended their lead just before the half-hour mark when Matej Vydra finished from outside the box from Wood's flick on.
However, Southampton responded well and were back on level terms before the break.
Stuart Armstrong fired past Nick Pope from a Danny Ings flick before the ex-Burnley striker capitalised on Ben Mee's error to make it 2-2.
The hosts completed the turnaround in the 66th minute when Theo Walcott lifted the ball to the back post and Nathan Redmond volleyed home.
Here are our RATINGS...
5. Ben Mee 5.6
Performed well in the air, but the skipper's lack of pace was often exposed. Handed Southampton an equaliser when allowing Walker-Peters' pass to run across him and Ings capitalised. Had a tough afternoon at St Mary's. Photo: Molly Darlington
6. Johann Berg Gudmundsson 5.2
Quiet. Didn't impose himself on the game anywhere near enough. Bertrand only troubled when the Icelandic international switched flanks with McNeil. Full of running, but fortunate to survive 90 minutes. Photo: Clive Brunskill
7. Dwight McNeil 6.2
Showed some delicate touches throughout the game, protected the ball well at his feet and brought others into play. Bust a gut to cut Walcott's break short in the second half and much more effective when switching to the right hand side late on. Photo: Clive Brunskill
8. Ashley Westwood 5.4
Started the game ever-so-well, breaking up the play, preventing the hosts from getting the ball out from the back and getting Burnley on the front foot. Couldn't get into it when Southampton got on top, but recovered in the final 10 minutes. Photo: Clive Brunskill