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.
13. Joe Gelhardt (sub)
6 - Wanted the ball, only received it a couple of times and not in areas where he could hurt Saints. Brushed off too easily a couple of times. Photo by Bruce Rollinson.
14. Crysencio Summerville
N/A - Came on in the final 10 but was faced with an uphill battle with Leeds playing so poorly. Photo by Catherine Ivill/Getty Images.
15. David Coote (referee)
7 - Didn't miss a lot, tried to let a niggly, stop-start game flow but it was a big ask. Photo by Nigel Roddis/Getty Images.