The Red Devils returned from the international break with a 12.30pm (BST) kickoff against the Saints at St Mary's.
Man United got off to a slow start and nearly found themselves behind when Southampton were awarded a penalty just after the half-hour mark.
However, Andre Onana pulled off a crucial penalty save to deny Cameron Archer and turn the momentum in Man United's favour.
The visitors wasted little time in opening the scoring through Matthijs de Ligt, before Marcus Rashford doubled the advantage in the 41st minute.
Alejandro Garnacho added a third in the 96th minute to wrap up a dominant display and Man United's second victory of the season.
Ten Hag hits out at Man United's schedule
While he was pleased with the result, Ten Hag criticised the Premier League's scheduling of early and late kickoff times.
Ten Hag told reporters: "First of all, for the fans it is very unfair to deal with this, with 8pm away games on a Saturday night, the 12.30pm, it's not right, but they are always there.
"I'm so proud of our fans that they are always there, whatever happens on the pitch they are always supportive of the team and there is a really good connection.
"They bring a very good ambience at Old Trafford and also at away games. I think the Premier League should pay some attention to this."
Saturday's fixture represented the second time this season that Man United have travelled to the South Coast for a lunchtime kickoff after they previously faced Brighton at 12.30pm on August 24.
Ten Hag laments scheduling disadvantaged
The Man United manager was unequivocal in his answer when asked about whether the scheduling is a disadvantage to his side.
'It's a big disadvantage," Ten Hag added. "But we have to deal with it as they did today. The team are mature, it doesn't matter, we always have to win, we can't bring any excuse."
Man United have a late kickoff for next weekend's Premier League fixture, with the Red Devils set to take on Crystal Palace at 5.30pm on Saturday.
Before that contest, the Red Devils will look to negotiate Tuesday's EFL Cup third-round tie against League One side Barnsley.