Marcelo Bielsa's Whites failed to muster a single short on target in the whole game in which they had just three attempts at goal.
The Saints bagged the only goal of the game in the 53rd minute when Armando Borja slammed home a fierce finish from the middle of the box to finish a rapid Southampton corner.
The defeat, United's fourth loss of the Premier League season, left the Whites fourth bottom.
Graham Smyth, the YEP's chief football writer, hands out the scores from an afternoon to forget at St Mary's.
1. Illan Meslier
5 - A couple of important saves. Distribution wasn't great but the options weren't great either.
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2. Liam Cooper
6 - Some big blocks as Saints dominated the first half. Battled well. The major problems were ahead of him.
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3. Pascal Struijk
4 - Not as assured as he has looked previously, some nervy moments. Redmond troubled him at times.
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4. Diego Llorente
5 - A couple of nice passes but still couldn't get Leeds playing and Redmond got in behind him to set up the goal.
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5. Stuart Dallas
3 - So far below his expected standards. Made a couple of big first half defensive interventions. Touch deserted him.
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6. Mateusz Klich
4 - Ran around, tried to press and tried to get Leeds moving but he was almost always outnumbered.
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