Manchester United made it two consecutive victories as a 55th minute goal from Bruno Fernandes was enough to see them through.
Man United had 56% of the possession with 6 shots on target.
Southampton also put a fight with 48% of the possession and 5 shots on target but David De Gea made sure United walked away with no blemish.
New signing Casemiro also came in the second half for his debut, showing flashes of brilliance.
United have now moved up to 6th place pending kick-off of other matches to take place on Matchay 4.