The returning Diego Llorente bagged the only goal of the game in the 18th minute when hooking home a finish from close range after a Raphinha corner.
The victory took Leeds out of the drop zone and on to six points after seven games played, three points clear of the bottom three and in 16th place heading into the October international break.
Southampton away is next.
Graham Smyth, the YEP's chief football writer, hands out the scores from Saturday's fixture at Elland Road.
1. Illan Meslier
7 - A spectator for much of it. There when needed but got away with dropping a corner. Photo by Alex Pantling/Getty Images.
2. Jamie Shackleton
8 - Solid, sensible performance. Battled well, got forward well in the first half. Photo by Alex Pantling/Getty Images.
3. Liam Cooper
8 - Really solid. Snuffed out any threat, headed and blocked everything he had to. Photo by Jan Kruger/Getty Images.
4. Diego Llorente
8 - A fantastic first half capped with an all important goal. Lasting the distance was important. Not as influential in the second but defended well. Photo by Alex Pantling/Getty Images.
5. Junior Firpo
8 - Up against the dangerman and never looked in any trouble. Got up the pitch to attack, played some nice stuff. Photo by Alex Pantling/Getty Images.
6. Kalvin Phillips
8 - Another one of those cruise control performances where he appears in full command. Some lovely passes to go with the defensive work. Photo by Jan Kruger/Getty Images.