© PA Photos
The visitors took the lead in comical circumstances with only three minutes on the clock thanks to Rodriguez.
However, United were level just three minutes later thanks to Wayne Rooney's 100th goal at Old Trafford.
The striker stroked the ball past Artur Boruc following a clever assist from Shinji Kagawa.
© AP Photos
Kagawa then came within inches of putting United ahead when his shot on the angle came back off the post.
The hosts finally got themselves in front on half an hour as Rooney converted from close range after Patrice Evra had headed Robin van Persie's free kick back across goal.
United ended the first 45 camped in the Southampton half, but they were unable to add to their tally despite chances for Van Persie and Danny Welbeck.