The Frenchman scored with a sublime volley to earn United a 1-0 win at Turf Moor and ensure Solskjaer's team head into Sunday's crucial clash with champions Liverpool three points clear at the summit.
"I've always said Paul is a big player for us," said Solskjaer. "He is a good character in the dressing room, he is always the one the lads look to and he's a world champion of course, and I think he's at his best at the moment."
It is the first time United have topped the Premier League in January since 2013, when Sir Alex Ferguson's team went on to win the title and victory at Burnley sets up a mouth-watering trip to Anfield on Sunday.
"What a brilliant position to be in," said Solskjaer. "We know it's going to be hard but we're ready and hungry which is good and we couldn't have asked for a better time to go there.
"We go there knowing we're playing the best team by a mile in the country in the last year and a half. We're looking forward to it and it's a great test of where we're at against a good team.
"Of course we know we're going to the champions, they've had an unbelievable three-and-a-half seasons so we know that's going to be a difficult game for us but we're ready for it."
After the match, Pogba said: "We know that the game today was very hard, very difficult and obviously we wanted to win.
"We know it's not easy to play here. We got the three points and we're happy for that, but there's still a long way and now we focus again until the end of the season."