Pogba started at Old Trafford despite returning to training this week following the World Cup, which he won with France in Russia a month ago.
United began strongly at home by winning a second-minute penalty after a handball from Leicester's Daniel Amartey.
Pogba stepped up and placed the ball in the top-right corner above Kasper Schmeichel.
Defender Luke Shaw then scored the first senior goal of his career to double United's lead before a late consolation from Leicester substitute Jamie Vardy.
Pogba lasted 84 minutes before being replaced by Marouane Fellaini, but Mourinho said he did not expect his French talisman to play for so long.
"We thought maximum 60 minutes but he managed over 80. The decision belonged to Paul - I asked him and he made himself available and he was very good.
"Paul's contribution was amazing but the fuel was disappearing."
Pogba meanwhile is trying to forget about his World Cup, which culminated in final success against Croatia in Moscow.
"I did not have any pre-season games - I came back on Monday and so it was very hard for the legs.
"Honestly, winning the World Cup is in the past. I like challenges and I want to progress and win more trophies."