The Cottagers grabbed ann early lead six minutes into the match at Craven Cottage through Ademola Lookman smart finish into the bottom corner.
But United responded well an pulled level thanks to Edinson Cavani capitalising on Fulham goalkeeper Alphonse Areola’s error before Pogba’s delightful curler from outside the area in the 65th minute banked the full three points.
“Of course you’d like a comfortable win at times but it never is easy down here. Of course going 1-0 down after such a short time, I think that was what we needed – we needed a wake-up call,” Solskjaer said.
“It’s never easy when you travel down here, stay in a hotel, you wanted to have a light training session but we couldn’t so we needed that wake-up call really.”
Leicester and Manchester City had moved to the summit over the last 24 hours, but the win sent the Red Devils two points clear and equalled the club-record 17 Premier League away games without defeat set by the treble-winning side of 1999.
Pogba was employed in United’s midfield at Craven Cottage, with his brilliant goal from distance his second in three games, and Solskjaer believes the French World Cup winner is in good form.
The United boss said: “He’s enjoying his football, he’s happy. Mentally he’s very happy and physically he’s in a very good shape and we know all about his talents.
“Today we decided to play him in midfield and it was worth it.”
Despite their early advantage, Fulham slipped to their second successive league defeat, while their winless run now stretches back eight games to leave them four points from safety.
The Cottagers were not without their chances in the game, but have struggled for goals this season, and manager Scott Parker bemoaned the missed opportunities.
“I think proud really but also disappointed, the players are also disappointed. We managed to get our noses in front and then a mistake and a screamer from a world-class player have defined the game,” Parker said.
“I think the overall factor is the big moments in the game, and I think we had the first big chance of the second half and a couple of big chances after that and they need to go in the net for us and you need to take those chances really.
“We didn’t manage to do that tonight and we probably haven’t managed to do that enough over the course of the last few games really.
“So it is certainly an area where we need to get better and we will do that.”