Second-half goals from Patrick Bamford, Stuart Dallas and Raphinha sent the Whites tenth - one place and one point above Arsenal. Leeds are now 13 points clear of the dropzone.
Graham Smyth, the YEP's chief football writer, hands out the scores.
1. Illan Meslier
7 - Some solid saves, one particularly smart one down to his right. A couple of crosses troubled him and a couple of passes went astray. Photo by Jon Super - Pool/Getty Images.
2. Diego Llorente
7 - Made a solid start, was justified in his reaction to the penalty award. Played a nice pass in the lead up to Bamford's goal. Should have scored one himself. Photo by Laurence Griffiths/Getty Images.
3. Liam Cooper
8 - Another good display in the Leeds defence. Unlucky not to score, again. Made some big blocks and tackles. Physicality was important. Photo by Gareth Copley/Getty Images.
4. Pascal Struijk
7 - Solid without being spectacular. A few nice touches and passes but battled hard to disrupt Southampton. Wasn't always successful in stopping them. Photo by Laurence Griffiths/Getty Images
5. Luke Ayling
6 - Not at his absolute best defensively but played some nice football going forward. Photo by LAURENCE GRIFFITHS/POOL/AFP via Getty Images.
6. Mateusz Klich
6 - A few tidy passes but couldn't stop Southampton in the middle in the first half. Limped out of the game before Leeds took control. Photo by Laurence Griffiths/Getty Images.