The Whites were 19th heading into the contest with their 20th-placed opponents, but Junior Firpo struck the winner in the 77th minute to secure a huge three points for Javi Gracia in his first match as head coach of the West Yorkshire outfit.
Ruben Selles, who will manage Southampton for the rest of the season, led the Saints to an impressive win at Chelsea last weekend, but the visitors remain bottom of the division on 18 points courtesy of the narrow loss on Saturday afternoon.
Both sides had half-chances in the opening 10 minutes, but Kamaldeen Sulemana dragged a shot wide for the visitors before Willy Gnonto had a strike blocked by Saints defender Jan Bednarek.
Luke Ayling was next to come close for Leeds, firing over the crossbar in the 18th minute, before Brenden Aaronson missed the target with a low strike when he might have slid a pass into Patrick Bamford.
The match was an end-to-end affair towards the end of the first period, with Jack Harrison just missing the top corner for Leeds in the 35th minute, before Illan Meslier made a smart save to deny Paul Onuachu down the other end of the field.
There were 11 goal attempts in the opening 45 minutes of action, but just two of those were on target - one for each team - with neither doing enough to deserve the lead at the half-time break.
Leeds had a shout for a penalty early in the second period when Bamford went down inside the box, but neither the referee nor VAR were interested, before the striker had a shot saved by Gavin Bazunu two minutes later.
The Whites managed to make the breakthrough in the 77th minute, though, with Firpo converting past Bazunu after Harrison's backheel had found his teammate in a dangerous position.
Crysencio Summerville should have added a second for the home side on the counter-attack late on, but the forward missed the post, with just the one goal separating the two teams in the relegation six-pointer.
Next up for Leeds is a trip to Fulham in the fifth round of the FA Cup on Tuesday, before returning to Premier League action away to Chelsea next weekend.
Southampton, meanwhile, will host Grimsby Town in the fifth round of the FA Cup on Wednesday, before welcoming Leicester City in the league next weekend.