Nathan Redmond scored his sixth goal in his last 10 games before Marcus Barnes levelled from the spot in a 1-1 draw after a handball was assessed against Jack Stephens in the 93rd minute.
Southampton took their deserved lead nearing the hour mark through a brilliant piece of individual effort from Redmond, who shifted the ball onto his right foot and fired a low shot into the corner.
Danny Ings, who was forced off through injury on 27 minutes, put Southampton on the front foot when he was denied one-on-one in the opening stages.
Southampton would twice be halted from a breakthrough with Shane Long having a shot cleared off the and James Ward-Prowse coming close to a fourth goal in as many games, before Redmond fired the visitors ahead.
Alex McCarthy preserved the lead with a point-blank stop against Barnes, before the forward struck the crossbar on 83 minutes.
Having been controversially denied a penalty in the first-half, it seemed just that Burnely would level from the spot after the ball struck Jack Stephens on the arm during an aerial battle with Peter Crouch.
Burnley: Heaton, Taylor, Mee, Tarkowski, Bardsley, Westwood, Cork, McNeil (Brady 81), Hendrick (Gudmundsson (58), Barnes, Wood (Crouch 76).
Unused subs: Hart (GK), Brady, Gibson, Vydra.
Goals: Barnes (PEN 90+4)
Bookings: Barnes (33), Bardsley (35), Mee (84).
Southampton: McCarthy, Targett, Stephens, Vestergaard, Bednarek, Ward-Prowse, Romeu, Slattery, Armstrong (Valery 77), Redmond (Austin 87), Ings (Long 27).
Unused subs: Gunn (GK), Jones, Sims, Elyounoussi.
Goals: Redmond (56).
Bookings: Targett (89).