The France international was handed his first start for the Red Devils since his £92m return to Old Trafford from Serie A champions Juventus last week.
While Pogba failed to get on the score sheet like his fellow new signing Zlatan Ibrahimovic, the 23-year-old midfielder impressed in the heart of Mourinho’s midfield.
The Champions League runner-up came close to sealing a dream second debut in the final minutes of the game but Pogba couldn’t direct his shot on target after Henrikh Mkhitaryan played his team-mate in.
But United manager Mourinho, who replaced Louis van Gaal at Old Trafford in May, still gave a glowing review of Pogba’s performance against the Saints.
“Paul Pogba was so good,” Mourinho told Sky Sports.
“He’s learning how to play with us. I’m very happy. [In some games] he can play even more offensively than he did today. He needs the freedom he had. I couldn’t be happier with him.”
Mourinho added: “In my opinion Marouane Fellaini was superb.”
United are three points clear at the top of the Premier League table after two successive victories over Bournemouth and Southampton.
The Red Devils will make the trip to promoted side Hull City in their next Premier League game on Saturday 27 August.
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