The £89m signing from Juventus played the full 90 minutes, 1,616 days after his previous appearance for the club.
He had more passes (71), touches (103), shots (4) and won more duels (20) than any other United player.
Mourinho said the France international had "such an ego, such a personality".
Zlatan Ibrahimovic scored both goals for United, to take his record to three Premier League goals in two games. He also scored in the Community Shield.
After the game Mourinho was asked about Pogba, the 23-year-old midfielder who left United for about £1.5m in 2012 to Juventus, before returning this summer.His first touch for the club since playing in a 5-0 win at Wolves in March 2012 saw him concede possession.
Mourinho told BBC Sport: "It just shows the personality of the player. His first match, his first touch was a bad one and led to a counter-attack and a free-kick and an opportunity for the opponent but he was not affected. The boy is fantastic."
Pogba, whose last game was France's Euro 2016 final defeat by Portugal, ran 11.2km, the third most of any player.
"He could have played 30 minutes more, he could have played extra-time, no problem," added Mourinho.
Pogba said: "It's a great feeling. I was relaxed, didn't have nerves and played my game. I came here to win, that is what I always wanted. It's a top club.
"The first ball, I lost it, but got used to it. After that I felt better, touched the ball and played with the team.
"We dream big. United are a big club. I know we will do big things this season."