Burnley captain Steven Caldwell scored the only goal to send Southampton closer towards the relegation zone.
The Clarets had not won away from Turf Moor since the start of February but Caldwell stooped to head home Robbie Blake's corner just before half-time.
That proved decisive with the visitors keeper Brian Jensen frustrating the Saints as Inigo Idiakez and Andrew Surman went closest to an equaliser.
Youssef Safri nearly scored with a last-gasp effort but could not convert.
Southampton boss Nigel Pearson:
"We are all bitterly disappointed and it is a tough result to take. I thought we deserved something out of that game because although we didn't play all that well we had a lot of chances, but you have to take them.
"I can't fault the players for their efforts and it is up to me to pick them up and keep their positivity to get something between now and the end of the season.
"For many people this result may seem like the club has hit a new low but it
is all in our hands to stay in this division."
Burnley manager Owen Coyle:
"To come here and get to win is very pleasing and although the play-offs are out of sight for us we still want to get as many points as we can before the end of the season.
"We want to increase our points total.
"With two games to go I want to see the same application and desire we showed today."
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