The victory came courtesy of goals in the last 20 minutes from Patrick Bamford and Tyler Roberts - the former netting his 16th of the campaign and the latter his first-ever in the Premier.
The Whites were tested by a Saints side that chased them down well in the opening half before running out of gas after the break when they could not keep going at Leeds' pace.
Head coach Marcelo Bielsa, who sprang a surprises when he started with Kiko Casilla in goal and gave Gaetano Berardi his Premiership debut as a half-time substitute, praised his players for the way they found a win to win.
He said: “We’re happy to have won and also with the consequences on the league table.
“Whoever scored first in this game was in better conditions to impose themselves.
“It wasn’t my influence, it was the profiles of the individuals in the second half who changed the game.
“The team in the second half looked a lot more like the team that it is, how we unlevelled the game in the second half. Southampton could have done the same in the first half.”
In the end United could have won by more than their two goals as they were denied a clear penalty and by some good saves by one-time Leeds loanee Alex McCarthy. Also on another day the home team would have been down to 10 men as James Ward-Prowse got away with an elbow on Diego Llorente in the first half.
But it was Southampton who had the better of things in the opening half. Although Leeds had skipper Liam Cooper back in their ranks they did not look as assured as in recent weeks at the back early on when the hosts threatened twice with Che Adams' header being tipped over by Casilla and Moussa Djenepo's chip from 40 yards out going close.
Theo Walcott rounded Casilla only to go a little too wide to get a shot away with his cross cleared by Cooper.
Luke Ayling was well wide with the Whites' first shot on 18 minutes before Stuart Armstrong did the same from distance at the other end.
The first bit of good football from United saw Stuart Dallas pull his shot wide after Jack Harrison's cross had been headed back by opposite winger Raphinha.
Llorente sent a header wide from a Kalvin Phillips corner, but Leeds were grateful to Casilla soon after as he tipped Adams' low shot wide.
The Leeds keeper got away with an error as he missed a corner, but Nathan Tella could not take advantage as he volleyed over.
Leeds were more in the contest after their poor start, however, with Rodrigo shooting over after turning on the edge of the box and shouts for a penalty falling on deaf ears after Ayling appeared to be contacted in the air by Mohammed Salisu as they both jumped for the ball.
Bielsa made two changes at the interval with Berardi on for Llorente and Pascal Struijk on to play in midfield instead of Phillips. On paper it looked to have weakened the Whites team, but not a bit of it as they went on to dominate the second half.
That was after they breathed a sigh of relief a minute in as James Ward-Prowse hit woodwork with a well struck free-kick.
Three minutes later McCarthy was forced into a smart save to deny Dallas who fired in a great volley from 20 yards out.
Bamford was then sent through by Rodrigo only to see his angled shot beaten away by McCarthy. The ball came out to Struijk, but his follow up shot was blocked by a defender.
A contentious moment followed when Bamford again raced through onto Raphinha's pass and attempted to round McCarthy. The keeper made contact with the visiting striker and not the ball, but as Bamford did not fall he was not awarded a penalty - and VAR man David Coote for whatever reason did not intervene.
Southampton occasionally looked dangerous with Ayling doing well to block Ward-Prowse's low shot and Danny Ings shooting over.
McCarthy was forced into another save, however, when Ezgjan Alioski got a shot in from inside the box after a great run and cross by Raphinha.
The deadlock was finally ended in the 73rd minute as Bamford got in behind the home defence onto Rodrigo's clever chip over and beat McCarthy to the ball to score from close range.
Saints tried to hit back with Nathan Redmond forcing Casilla into a save and Ings sending a near post header over, but United came close to a second when Raphinha cut in from the right to send a shot just over.
Two more efforts followed from Redmond that did not trouble the visiting keeper while Ings volleyed wide from the edge of the box and Jack Stephens could only direct his close range header straight at Casilla.
In a thrilling finish it was Leeds who did score again in added time when Roberts produced a calm finish after initially dwelling too long on being sent clear by Raphinha. Although he was tackled, Bamford followed up to get in a powerful shot that was blocked only to fall for the Welsh international who gleefully netted his first goal for a year.
United almost put the icing on the cake when Southampton were carved open again and Raphinha was only denied by another fine McCarthy save.
In the end it was a fully deserved three points for Leeds who for 24 hours at least are up to eighth place. They have now sealed a top half finish in the Premier for the first time since the 2001-02 season.
(Bamford 73, Roberts 90+5)
Southampton: McCarthy; Walker-Peters, Vestergaard, Stephens, Salisu; Walcott (Diallo 78’), Ward-Prowse, Armstrong, Djenepo; Tella (Redmond 70), Adams (Ings 45’).
Leeds: Casilla; Ayling, Llorente (Berardi 45), Cooper; Phillips (Struijk 45), Dallas, Alioski; Raphinha, Rodrigo (Roberts 79), Harrison; Bamford.
Referee: Peter Bankes