Samuel Umtiti found the net with a powerful header in the 51st minute of the semi-final to book Frances place in the final against either Croatia or England.
Didier Deschamps side were under pressure for much of the game, with Belgium having 64 per cent of possession St Petersburg, but NGolo Kante and Pogba impressed in midfield for the 1998 champions.
Manchester United boss Mourinho hailed Pogba and also singled out Raphael Varane for his display against Roberto Martinezs men.
While Pogba got on the wrong side of Mourinho on more than one occasion at United last season, his assured performance pleased the Portuguese on Tuesday evening.
They tried to control the game which they did with a fantastic performance by Varane and a very good performance by Pogba, Mourinho told RT following Frances victory.
Pogba was mature he played with great maturity. When he had to hold position and to keep control of the game he did.
When Deschamps took off [Olivier] Giroud to bring on [Steven] Nzonzi then Pogba had more freedom but freedom not to do silly things. Freedom to keep the ball away from the dangerous areas.
To keep the ball, to assist [Antoine] Griezmann for a great chance. He was very, very mature.
Mourinho revealed that he predicted the semi-final would be lacking in goals before kick-off.
In the end I think the result was 1-0 but it could be 0-0 or it could be 1-1 and we could have been waiting for extra time but since the beginning I was smelling this, he said.
I was smelling a match without many goals that was good by the emotion that involves a semi-final but it was not an especially good football match.