The Norwegian has overseen 10 wins from his 11 games at the helm and he made six changes in west London with one eye on his first taste of managing the Red Devils in Europe.
Pogba stole the show but Martial impressed on his recall with Diogo Dalot, Phil Jones and Chris Smalling helping to keep a clean sheet after coming back into the side, with Romelu Lukaku and Juan Mata also given a chance to impress.
But for Murphy, Fulham’s problems were all their own doing.
Fulham’s poor decision-making
Murphy pointed out the poor decision-making early on as the first catalyst to their downfall.
Showing a moment where Anthony Martial pressed high on Denis Odoi, who was saved by the ref’s whistle for a soft foul, the pundit said: “When you play a team of Manchester United’s quality, especially with the forward players they’ve got, the last thing you want to do is help them.
“You’ve got to make right decisions. Look, Martial is behind him here. He’s waiting and saying ‘please play him this pass, please give Odoi the ball and I’ll get after him’.
“It’s a bad ball, a bad decision, then he’s taken too many touches, he could have gone back to the keeper and he gets away with it again.
“That just brought United on to them and it gave them confidence.”
Man Utd’s first goal
Pogba now has eight goals and five assists since Solskjaer took the reins – two of his strikes came against Fulham.
But he was helped, on his first, by some rookie defending. Anthony Martial slipped a reverse pass into Pogba, who beat a hapless Sergio Rico from a tight angle.
“For the goal, Chambers sees Pogba too late. Pogba’s your midfield man, he’s going to be the one going forward,” Murphy said.
“As for the goalkeeper, we better not go there. That’s really poor.”
Poor positioning for Man Utd’s second
Martial had the beating of Odoi and Maxime Le Marchand for a stunning second goal – but it was the former whose display irked Murphy the most.
“Odoi, I don’t know why he’s so high up but he tries to recover,” he said. “He gets back in, doesn’t make the tackle and doesn’t do anything. He had an absolute nightmare today.
“It’s a brilliant goal but I’m analysing Fulham and the problems they give themselves in games. They may be willing to go forward but they give themselves problems defensively.”