Romelu Lukaku scored the third goal and set up the second, while David de Gea made an important save in the second-half after being untroubled in the first-half and the clean sheet against the Toffees was the Spaniard's 100th for United. Ander Herrera was the third player on the manager's list despite the midfielder playing just 13 minutes as a second-half substitute.
The Red Devils were on the front foot right from the start and Antonio Valencia's fourth-minute thunderbolt put them ahead and it remained that way until the 83rd minute. The Toffees were a much better side in the second-half and had more possession overall, but late defensive errors cost them a chance of any points.
It took United until the 83rd minute to get the second when Lukaku collected a misplaced pass from Ashley Williams and set up Henrikh Mkhitaryan. The third and the fourth came soon after with the Belgian striker adding his fifth in as many games for United and Anthony Martial added the final goal from the penalty spot.
Mourinho was delighted with Lukaku's performance but made it clear that he would have been happy even if he did not score, as his work rate and understanding of the manager's tactical plan is sufficient. De Gea was also praised for being focused through the 90 minutes despite being largely untested until the second-half.
"I would be pleased even without that. The work he does for the team, the way he opens spaces for us in the first half, I was more than pleased. One more goal, fantastic, one assist. But his overall work is more than that," Mourinho said of Lukaku after the win, as quoted on United's official site.
"It is more difficult when you are sleeping. You don't touch the ball for minutes and minutes and minutes and then have an important moment in the game. So it's even more difficult and even more important," the Portuguese coach added about De Gea.
Herrera, on the other hand, was a surprise inclusion in the manager's list, as the midfielder has been sparingly used this season. He has fallen down the pecking order and is behind Paul Pogba, Nemanja Matic and Marouane Fellaini for a place in midfield.
The 28-year-old has played just 90 minutes of Premier League football thus far this campaign, but was praised by Mourinho for his 13-minute cameo during the win over Everton. It was after Herrera arrived that United scored their second, third and fourth goals and the manager believes he brought stability to the game and ensured Ronald Koeman's side had no chance to get back into the contest.
"I think Ander was important," Mourinho added, as quoted on Manchester Evening News. "He gave us the stability that we were losing a little bit and then was only possible, in my view, 1-0 or 2-0, I never thought in the last 15 or 20 minutes it could be 1-1."
"The 2-0 come and after that the third and fourth goals are just a consequence of a team that was sad and another team that was happy, for me the third and fourth goal were a little bit out of context in the game," he explained.