The two sides came into the game level on 33 points and Burnley charged in front in a thrilling first half at a sunny St Mary’s Stadium.
Chris Wood fired in an early penalty, awarded after the video assistant referee advised Andre Marriner to check the pitchside monitor, before knocking down Ben Mee’s long ball for Matej Vydra to volley in a fine second goal.
But Southampton, who welcomed back Danny Ings and Theo Walcott from injury, hit straight back with midfielder Stuart Armstrong sweeping in the ball after a neat flick by Ings.
The ex-Burnley striker coolly slotted in his 10th goal of the season to equalise just before half-time, scoring against his former club for the third successive game.
And although Burnley’s Nick Pope pulled off some fine saves after the break, Saints broke the England goalkeeper’s resistance as Nathan Redmond volleyed them in front.
The hosts then needed some goalkeeping heroics from former England keeper Fraser Forster, who twice denied Wood late on, before clinching just their second win in 13 Premier League games.
That lifted Ralph Hasenhuttl’s men up to 13th in the table, 10 points clear of the relegation zone with eight games left.