Edinson Cavani played an integral role in the fightback, with the Uruguayan scoring twice to help United cart home all the three points.
Both teams came into the match in fine shape, with Southampton in particular, picking a number of wins to find themselves in the top four.
United, on the other hand, have witnessed a somewhat mini-revival after a stuttering start to the new season.
Ole Gunnar Solskjaer’s men were out in search for their fourth straight win in all competitions, having won 4-1 in their last fixture against Istanbul Basaksehir in the Champions League.
However, it was clear Southampton were not to going to be pushovers given they were unbeaten in seven Premier League games in the run up to the Sunday tie.