Mauricio Pochettino’s side started the game with energy and a high intensity and could have taken the lead early in the first half.
Jay Rodriguez sent a warning to the home side when twice heading wide and Dani Osvaldo really should have done better when the ball dropped to him on the edge of the area after Victor Wanyama robbed Wayne Rooney of possession deep inside the United half.
It was the home side who took the lead though when Robin van Persie scored United’s first goal from open play at home in the Premier League this season.
It was a slow start from the champions but Adnan Januzaj’s sublime pass to Wayne Rooney provided the England forward with the chance to score. Artur Boruc smothered well but the danger was not cleared and Van Persie converted expertly from a tight angle.
The goal appeared to give the home side and the fans a lift.
Moments after Van Persie’s opener Nani found space on the right and his cut-back to Rooney cannoned off the crossbar.
After the break United went in search of that killer second but Van Persie could only flick Rooney’s expertly taken corner onto the bar.
Man of the moment Januzaj then tested Boruc from distance but the giant Polish keeper stood firm and his solid arm diverted the ball to safety.
Southampton then regained control of the ball and the game.
Osvaldo again failed to hit the target from the edge of the area and, when he eventually got the better of Phil Jones in the air, he could not direct his header at goal.
But, when it looked like United were going to hang on for all three points, Dejan Lovren caused mayhem in the United penalty area and his effort cannoned off Lallana and into the empty net.
The goal was a fitting reward for the travelling fans but for United further questions will be asked of Moyes after more vital points are dropped at home.