Pogba scored twice as Manchester United made it two wins in two for Solskjaer.
United beat Huddersfield 3-1 to close the gap on the four to eight points.
And things are already looking better for Pogba under the new boss who looked set to leave until Jose Mourinho was sacked.
But Solskjaer reckons Pogba is happy where he is.
Solskjaer said: “That’s the Paul I know and have known since he was in the reserves and youth team here.
“He’s always been a happy boy with a big smile on his face and when you score two goals you’re happy and should be.
“It’s a privilege and a responsibility playing for Manchester United and Paul loves playing for this club.
“He’s Manchester United boy through and through and knows what it means to play for Manchester United.
“Last time he created two or three goals and this time he scored two himself. I think he’ll enjoy this tonight.”
Pogba helped Solskjaer make it two wins from two under his caretaker reign and the Norwegian admitted it was emotional being back at Old Trafford a decade after his testimonial.
“It was extra special, but I was surprisingly calm,” he said. “The boys have settled me down really quickly and you trust the team you put out.
“It’s special hearing the crowd singing my song. Usually it was when I scored, but they started when the game began.
“It’s humbling and it makes you really proud and for my family and family back in Norway, watching on TV. It’s a day I’ll never forget.”