David De Gea 7/10 - A quiet night for De Gea, who only had one save to make. The Spaniard's lack of activity shows how much Mourinho has improved Manchester United defensively.
Antonio Valencia 8/10 - A constant threat down the right-hand side, Antonio Valencia played most of the game as a winger and caused countless problems for the Saints.
Eric Bailly 7.5/10 - Another solid performance at the back for Bailly, who faced a more challenging test with both Shane Long and Nathan Redmond trying to run in behind. Bailly's pace ensured United kept a clean sheet.
Daley Blind 7.5/10 - Like Bailly, another calm showing at centre-back for Dutchman Blind. The 26-year-old seems to be forming a strong partnership with the Ivorian defender.
Luke Shaw 8.5/10 - Shaw continues his comeback from a broken leg, and it's starting to look like he has never been away. The Southampton graduate got up and down the flank, and won the penalty for United's second.
Marouane Fellaini 8/10 - A player who looked like he would not have a future when Mourinho arrived, Fellaini provided a shield in front of the defence, and his willingness to sit in allowed Pogba to express himself.
Paul Pogba 8/10 - On what was his first Premier League start for Manchester United, Pogba gave fans a glimpse of why United paid a world-record fee for his services. A classy performance in the middle of the park.
Juan Mata 7.5/10 - Mata will be looking worryingly over his shoulder with Henrikh Mkhitaryan lurking, but the Spanish midfielder put in another strong showing, linking up with Ibrahimovic well.
Wayne Rooney 7/10 - With all eyes on Zlatan and Pogba, Rooney went under the radar at Old Trafford. The United captain put in a wonderful cross for Ibrahimovic to head home, but that was as good as it got for Rooney.
Anthony Martial 7/10 - An odd performance from Martial. The first half was a shocker for the Frenchman, but he burst into the game after half-time, and should have capped off the evening with a goal.
Zlatan Ibrahimovic 9/10 - Man of the match. The presence of Swede alone is enough to terrify defenders, and Southampton could not deal with his power. Ibrahimovic was the perfect target man, and is rightfully the Premier League's top scorer so far.
Henrikh Mkhitaryan (Mata 76) 7/10 - The Armenian looked lively when he came on, and will be hoping to force his way into the starting XI in the coming weeks.
Ander Herrera (Martial 82) n/a - The Spanish midfielder was dropped for Pogba, and did not have enough time to make an impact.
Chris Smalling (Rooney 89) n/a - The England international did not have enough time to make an impact.