A second-half volley from Bruno Fernandes was enough to separate the sides at St Mary's, earning Ten Hag his first competitive away win since taking charge of the Reds in the summer.
The boss named an unchanged line-up from Monday's win over Liverpool, and despite clear-cut chances being at a premium for both teams, United found the breakthrough and defended valiantly to take a valuable three points back to Manchester.
New signing Casemiro came off the bench in the second period to make his debut for the club and helped to shore up the midfield and defence as the Reds shut out our hosts effectively.