Patrick Bamford and Tyler Roberts were on target as Leeds United secured a third straight victory and climbed to eighth, staying in the fight for European qualification.
Leeds goalkeeper Kiko Casilla tipped a Che Adams header over the bar in the opening minutes and later palmed away another effort from the striker as Southampton started well in front of 8,000 home fans.
The visitors' best chance of the first half fell to Stuart Dallas, who controlled the ball on his chest before shooting wide just inside the box.
Saints' James Ward-Prowse clipped the bar with a free-kick soon after the break, while Alex McCarthy denied Dallas and Bamford in quick succession at the other end.
But Bamford beat McCarthy with 17 minutes left, latching on to Rodrigo's pass and finishing between the goalkeeper's legs for his 16th Premier League goal of the season.
Roberts then struck for the first time in the competition, reacting quickest when Bamford's stoppage-time shot was saved and slotting into the bottom corner.
Leeds' 10th away win of the campaign, which is a club record in the Premier League, takes them to 56 points, three behind Spurs and West Ham United in the battle for European places, although the London clubs each have a match in hand and better goal difference.
Southampton stay 14th with 43 points.
Southampton: 23 May v West Ham (A)
Leeds: 23 May v West Brom (H)
Referee: Peter Bankes. Assistants: Neil Davies, James Mainwaring. Fourth official: Kevin Friend. VAR: David Coote. Assistant VAR: Marc Perry.