Ronald Koeman's men suffered their fourth consecutive defeat in a poor performance at Turf Moor, with Ashley Barnes punishing the winger's miss to give the hosts a boost
Sean Dyche's side were the better team for large portions of the match, though might count themselves lucky that Michael Keane was not sent off for a crunching tackle that put an early end to Saints youngster Jake Hesketh's first start.
The visitors had a golden chance to get back on track on the hour when Ryan Bertrand was brought down in the area but Dusan Tadic's spot kick was saved well by Tom Heaton.
And Ashley Barnes punished them with a deflected shot that wrong-footed Fraser Forster to give the hosts the points at Turf Moor.
|VIEW FROM TURF MOOR
|By Pete O'Rourke
What a big win this could prove to be for Burnley come the end of the season and they just about deserved it.
In a scrappy game the Clarets just about did enough to claim all three points through Ashley Barnes's deflected effort 17 minutes from time, after Dusan Tadic had missed a great chance to give Southampton the lead on the hour mark when he saw his penalty saved by Tom Heaton.
The win moves Burnley out of the bottom three while, for Southampton, it is their fourth defeat on the spin and Ronald Koeman will be left to rue that penalty miss as he makes his way back to the south coast.
Burnley, unchanged from their loss to QPR, threatened twice in the opening three minutes through Danny Ings, who failed to make a telling connection to George Boyd's cross before flashing a 25-yard drive narrowly wide.
The home side went close to an opener again in the 26th minute when Forster reacted smartly after Nathaniel Clyne had deflected Kieran Trippier's cross goalwards under pressure from Barnes.
Hesketh, booked earlier for sliding in late on Heaton, saw his maiden start curtailed in the 32nd minute. Following a heavy collision with Keane, the 18-year-old hobbled off and was replaced by James Ward-Prowse. The substitute was making his first appearance since September, having recovered from a fractured foot, and soon tested Heaton with a low shot five minutes before the interval.
Following a quiet start to the second period, Sadio Mane sent his shot over the crossbar following some neat interplay from Southampton, who then passed up a golden opportunity to break the deadlock.
After Boyd had tripped Ryan Bertrand in the left-hand corner of the area, Tadic struck his penalty well but Heaton was equal to it to preserve his clean sheet.
Burnley responded, Ings forcing a smart low save from Forster before Barnes provided the crucial breakthrough. Ings charged down Clyne's clearance and the ball ran kindly for his strike partner, who slotted beyond Forster with the help of a deflection off Alderweireld.
Clyne almost atoned for his part in the goal when he fired a drive narrowly past Heaton's right-hand post three minutes from time but that proved to be Southampton's last meaningful effort as Burnley held on for a precious victory.