The Clarets could have moved into the play-off places had they been able to secure back-to-back wins at Turf Moor.
But they gave themselves too much to do after Southampton stormed into an early 2-0 lead.
Chris McCann pulled a goal back before the break, but when the Saints restored their two-goal cushion six minutes into the second half Burnley were facing an uphill battle.
Substitute Ade Akinbiyi instigated a tense finale with his fourth of the season eight minutes from time, as chances were created at either end.
But George Burley's men held on for their third away win of the season.
Burnley, looking for back-to-back wins, had their game plan distorted after just three minutes when an unmarked Bradley Wright-Phillips burst on to Christian Dailly's perfectly weighted ball over the top of the defence and got the better of Gabor Kiraly in a one-on-one.
Southampton could even have been 3-0 up within the first 14 minutes, but Stern John and Wright-Phillips were both denied by the woodwork.
But Saints didn't have to wait long for their second breakthrough, capitalising on some poor defending as Jason Euell rose high above Graham Alexander at the far left-hand post to head home Nathan Dyer's cross from close range.
McCann's sweet long-range strike just after the half-hour gave Burnley hope going into the break.
But John jumped high above McCann to meet Phil Ifil's right-wing cross with a header at the far post to make it 3-1.
Akinbiyi offered hope to the Clarets, but it was too little, too late.