The France international's performance was pivotal against the Blues, setting up Anthony Martial's opener and laying on the second goal for Jesse Lingard - though the forward virtually created it himself with a solo dribble to make space on the edge of the area.
His pair of assists takes his tally for the season to seven in just 12 Premier League games this term, added to three goals, having contributed just four assists in 30 top-flight matches last term.
Pogba's influential display came after comments from ex-United midfielder Scholes last week in a home draw with Southampton in which he questioned the £89 million man's work-rate and attitude.
Yet Mourinho distinctly disagreed with the BT Sport pundit and went both barrels at the 43-year-old for being overly harsh on Pogba's performances.
Mourinho: Pogba always tries his best
In defence of Pogba, Mourinho told reporters at Goodison Park: "I think the only thing Paul Scholes does is to criticise. I don't think he comments, I think he criticises, which is a different thing.
"Not everyone of us has to be phenomenal like he was as a player. He was a phenomenal player, that doesn't mean that we all have to be phenomenal.
"Paul [Pogba] tries to do his best all the time. Sometimes he plays very well, sometimes he plays well, sometimes he doesn't play so well. You know, it's not Paul's fault that he much more than Paul Scholes. It's just the way football is.
"But I think Scholes will be in the history as a phenomenal player, not as a pundit.
"I prefer to look at him as a phenomenal player that gave so much to the club that I am proud to represent and to give my whole contribution every day. Every day I try to do my best."
"I hope he is successful if he ever manages"
The Portuguese boss was not in any way subtle of his scolding of Scholes, who made 718 appearances for United and won 25 trophies across a 20-year senior spell at Old Trafford.
While he named Scholes as one of the best midfielders he has ever seen, the United boss mockingly suggested that Scholes would love to be as successful a manager as he has been.
Mourinho said: "If Paul [Scholes] one day decides to be a manager I wish that he can be 25 per-cent as successful as myself, because 25 per-cent of 25 is six trophies. I think he'd be quite happy.
"In my mind, Paul Scholes [is a] phenomenal player [and] one of the best players I have ever seen playing in midfield.
"He gave so much to my club that I only can thank him for that because the prestige of this club is based on people like him, so successful here."
On what it is with former United players coming out to criticise the club's current team, Mourinho added: "I think they would love to be here, they would love to be in the club. That's a problem that I cannot resolve."