It wasn't a routine win as Southampton piled on the pressure in the second half, and Jose Mourinho had to throw in Chris Smalling and Daley Blind to ensure United leave the St.Mary's Stadium with all three points. Here's how the Manchester United players fared.
Goalkeeper and Defence
David De Gea: Didn't do much on the day, as the defense put in a solid performance to gift the Spaniard his fifth clean sheet in this campaign. (7/10)
Ashley Young: Was part of the defensive setting that excelled on the day, and it was his cross from the left that Romelu Lukaku benefited from to score United's only goal at Southampton. Had a nice game. (8/10)
Phil Jones: Arguably United's best player in the match, constantly obstructing the opposition's attack. Was on hand to block Oriol Romeu's shot; that was destined for the net - with David De Gea well beaten - in the early stages of the second half. Top Performance from the Englishman. (10/10)
Eric Bailly: Did well to ensure United remain unbeaten, as well as helping the defense with another clean sheet on the day. Bailly put in a decent shift. (8/10)
Antonio Valencia: Couldn't score a screamer as he did last weekend against Everton and didn't show much in attack, but he had a decent performance at the back. (7/10)
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Midfield and Attack
Nemanja Matic: Was hardworking in midfield, doing well to help out with defensive duties in United's box also. He wasn't as superb as he was against Everton last weekend, but he wasn't bad either. (7/10)
Marouane Fellaini: Was at the right place at the right time to clear Romeu's header off the line as Southampton piled on the pressure in the second half. Occasionally helping to avert dangers in the box - when the opposition attacked through set-pieces. That's another fantastic performance from the Belgian on the trot. (8/10)
Henrikh Mkhitaryan: Impressed in the game, especially in United's link-up play in the attacking third. Had to be sacrificed for Smalling in the 75th minute, as United fortified their defense against Southampton's second half squeezing. (7/10)
Juan Mata: Didn't offer much from the right, as he fancies the attacking midfield position. Couldn't influenced the game much from that position. But was helpful in United's build-up play until his withdrawal in the 62nd minute. (6/10)
Marcus Rashford: Almost had United's second: as his free-kick curled just inches wide. Tormented the opposition with his pace, but was withdrawn for Blind in added time. (7/10)
Romelu Lukaku: Showed why United paid heavily to secure his services to score his sixth league goal and his eighth for United in all competitions so far in the season. Was impressive for United on the day, and was easily United's second best player on the pitch (after Jones) - just as United's Match Day poll on Twitter suggested. (9/10)
Ander Herrera: Came on in the 62nd minute for Mata and, did his bit to ensure United survive Southampton's second half pressure. Though should have done better with the chance that came his way in the opposition's box: unmarked, and with ample time to score United's second, the Spaniard fired over the bar. (5/10)
Chris Smalling: Introduced for Mkhitaryan in the 75th minute, the Englishman helped United see out the game, as United took all three points from the encounter. Meanwhile, the time spent on the pitch wasn't enough to earn him a rating.
Delay Blind: Came on in the 92nd minute for Rashford as Southampton probed United laboriously for a late equalizer.