The Frenchman put the Red Devils 1-0 up against Everton before half-time as they went on to win 2-1 at Old Trafford.The £89m man saw his initial effort from the spot saved by Jordan Pickford after a bizarre run-up, but he netted the rebound.
Anthony Martial doubled their lead before Chris Smalling hacked down Richarlison in the box to let Gylfi Sigurdsson claw one back.
But United held on to manage just their second win in seven games to alleviate some of the pressure on Mourinho.
And the 55-year-old boss Mourinho was happy with his team despite their late hiccup.
He said: ”I am happy again. It was a game we didn’t need to suffer as much in the last few minutes. We had it under control even when it was 2-1.
“The last ball of the game is a corner and anything can happen but we played well and in some periods we played very well. When we had to fight and give everything to get three points, the players were able to do it.”
And on the penalty decision, Mourinho went on to explain that Pogba is more of an expert on them than he is.
He added: ”I think the referee was very good in all the game. He was solid and consistent. In the two penalty actions he was consistent.
“Pogba is a better penalty taker than myself. He has the courage to take it. Luka Milivojevic missed one and he took them today. I admire players who have the courage to take them.
“He wants to take them. Maybe he has to change his approach but I don’t want him to change his mental approach.
“The keeper is also a good penalty saver soletsgive credit to him. He showed that in the World Cup.”
Meanwhile, Pogba revealed he was lucky to have scored his penalty after seeing his effort saved.
He said: ”We needed to win, we needed points. The last game against Chelsea, we should have won this game, we missed two points.
“Today we needed to win, needed to come back totopof the league.”
“I was lucky [with the penalty], the important thing is it went in and I scored the goal, good for us and me.
“After we carried on and had other chances, most important thing was the win.”