Substitute Sam Vokes was the hero for Burnley as they came away from St Mary's Stadium with a 1-0 win that sent them sixth in the table.
After a first half where both sides threatened but failed to find a breakthrough, Burnley manager Sean Dyche turned to Vokes in search of a winner midway through the second half.
And his move paid off in the 81st minute as Vokes headed a Johann Berg Gudmunsson cross past Fraser Forster into the bottom-right corner of the goal.
The result drops Southampton to 13th with 13 points.
Southampton: 18 Nov v Liverpool (A)
Burnley: 18 Nov v Swansea (H)