The two sides went into the half-time interval all square, but Marcelo Bielsa's men took the game away from their out-of-form visitors with a dominant second-half display.
Patrick Bamford opened the scoring with his 13th of the season two minutes after the restart before further goals from Stuart Dallas and the brilliant Raphinha in the final 15 minutes wrapped up a return to winning ways for Leeds after back-to-back defeats.
Southampton would have been aggrieved by a penalty which was overturned by VAR in the first half, in addition to a disallowed goal after confusion over when the referee blew his whistle.
However, they were comfortably second best in the second half as they slumped to their seventh defeat during an eight-match winless run - the longest such ongoing streak in the division.
The result leaves the Saints 14th in the table, eight points clear of the relegation zone, while Leeds have taken full advantage of their game in hand to climb above Arsenal into 10th.
25th min: Raphinha breaks into the box from the right flank before teeing the ball up for Tyler Roberts, who fires well over from inside the area when he should do better.
27th min: Raphinha drifts a free kick into the box which Diego Llorente nods back into a dangerous area. Southampton are unable to clear their lines and Liam Cooper gets his boot to the ball, but his improvised effort is deflected over the crossbar.
33rd min: Tella dribbles into the box from the left channel before going down under the challenge of Llorente inside the box, prompting referee Andre Marriner to point to the spot.
VAR official Kevin Friend tells Marriner to go and look for himself on the monitor, and the referee overturns his on-pitch decision after deeming that Tella initiated the contact.
39th min: Raphinha races clean through on goal via a counter-attack from a Southampton corner and looks certain to score when one on one with the keeper, only for Oriol Romeu to produce a goal-saving last-ditch challenge in the area.
44th min: Southampton have the ball in the back of the net as Che Adams sweeps home a smart, quickly-taken free kick from Ward-Prowse. Andre Marriner quickly pulls play back, though, claiming that the free kick had been taken moments before he blew his whistle, much to Southampton's dismay.
46th min: Nathan Redmond finds a yard of space inside the box and gets his shot away, but powers it straight at Meslier.
47th min: Patrick Bamford opens the scoring with a pinpoint and precise finish into the bottom corner, beating Alex McCarthy in the Southampton goal with accuracy rather than power.
Roberts slips the in-form striker through with a defence-splitting pass through the middle, and Bamford takes a touch before steering the ball into the bottom corner off the post.
49th min: Southampton almost produce an immediate response as Stuart Armstrong darts in from the left channel and almost sneaks his finish in at the near post, but Meslier is down smartly to make a good one-handed stop.
50th min: Leeds almost make it two in reply as Raphinha finds Roberts on the edge of the box, only for the midfielder to steer his effort inches wide of the post with McCarthy beaten.
53rd min: The action-packed start to the second half continues as Stuart Dallas breaks forward before finding Bamford, who fires his effort straight at McCarthy when he should have doubled his personal tally for the night.
61st min: More fine play from Raphinha down the left as he dances into space before playing a low ball inside to Llorente, who should score but sees his close-range effort brilliantly saved by McCarthy.
77th min: Leeds double their lead with a sweeping counter-attack, completed by a smart Stuart Dallas finish.
Helder Costa ignores the run of Raphinha to tee up the Northern Ireland international, who takes a touch before picking out the corner with a toe-poke.
84th min: Raphinha puts the game well and truly to bed with a fine free kick into the bottom corner, which McCarthy gets a hand to but cannot keep out.
91st min: Leeds look to add a fourth late on as Pablo Hernandez attempts an audacious volleyed effort with the outside of his boot, but he gets it wrong and it skews wide of the target.
MAN OF THE MATCH - RAPHINHA
Raphinha really came into his own in the second half, taking the game away from Southampton with a constant threat down the wing and giving makeshift right-back Jan Bednarek in particular a torrid time.
The attacker was not directly involved in either of the first two goals but, even before he capped off his display with the third, he was the standout performer once again for Leeds.
Oriol Romeu's challenge on Raphinha may not have been worth anything in the end, but it was still a stunning piece of defensive work to prevent what looked like a certain opening goal for Leeds.
Even catching Raphinha, who had raced clear and appeared to have all of the time in the world, was impressive enough, but to then time his tackle to perfection was brilliant.
If awards were given for tackle of the season, this would be a front-runner.
Possession: Leeds 47%-53% Southampton
Shots: Leeds 11-13 Southampton
Shots on target: Leeds 7-5 Southampton
Corners: Leeds 2-4 Southampton
Fouls: Leeds 11-13 Southampton
LEEDS (3-3-3-1): Meslier; Llorente, Cooper, Struijk; Ayling, Klich (Alioski 59'), Dallas; Harrison (Helder Costa 46'), Roberts (Pablo Hernandez 75'), Raphinha; Bamford
SOUTHAMPTON (4-4-2): McCarthy; Bednarek, Vestergaard, Salisu, Bertrand; Armstrong, Ward-Prowse, Romeu (Djenepo 70'), Tella (Minamino 58'); Adams, Redmond (Ings 58')