Having taken the lead through Romelu Lukaku's goal, United dominated the first half and looked set for another routine afternoon on the south coast.
In the end, however, it proved anything but as Saints took control after the break and, in truth, deserved an equaliser on the balance of play.
United have been scoring goals for fun having plundered 24 in all competitions, but this was the hardest fought of victories, and one that came straight from the Jose Mourinho away-day textbook.
A performance of organisation, resilience and dogged defending to hold out for a huge, if scarcely deserved win, one that keeps United clinging to the coat-tails of free-scoring neighbours City.
The hallmark of potential champions is the ability to grind out results when not at your best and to win ugly when required.
In a match from which points would have been dropped last season, that's exactly what we managed to do at St Mary's.
The Reds miserly defence has conceded just two goals this season and was given its sternest examination so far as Southampton piled on the pressure with an aerial bombardment in the second half.
It was testament to the performances of centre-backs Phil Jones and Eric Bailly that, for all the hosts possession and territory, David de Gea only had one save to make.
United's attacking players have, rightly so, been getting the plaudits for a prolific start to the season, but the Bailly - Jones partnership has been just as important.
United have won five out of six league games with the pair having kept a clean sheet in all but one of those, with the 2-2 draw at Stoke the only aberration.
Jones' ability has never been in question and, in a United career hit hard by injury, he finally seems to be holding down a regular place in the side.
The England man was voted our man of the match and played a huge role in keeping resurgent Saints at bay during a second half in which United had to dig deep.
Such was the prolonged pressure that Jose reverted to a five-man defence and introduced Chris Smalling off the bench as a third centre-back to play alongside Jones and Bailly.
Throughout his immense performance, Jones kept Shane Long frustrated, as he denied the pacy striker the service that was being pumped into the box from wide as well as from midfield.
Not pretty, but a win as important as any other this season.
United roll on..