United were largely untroubled throughout at Goodison Park - with David De Gea not forced into a single save - but struggled to carve out their own opportunities.
Yet they turned on the style in the first half and after Juan Mata struck the post, Anthony Martial curled in from 20 yards to put the visitors ahead.
While that summoned a brief response from Sam Allardyce's Everton, United put the game beyond the Blues through Jesse Lingard - also netting a gorgeous curling effort beyond Jordan Pickford.
And Mourinho felt that the performance that his side produced to end a run of four top-flight games without a win was one in which they got better and better as the match progressed.
Red Devils "played very well"
"I think we played very well, second half better than the first. Second part of the first half better than the first half of the second half," Mourinho analysed afterwards.
"I think we were always improving from minute one until minute 70, we were always improving, improving, improving. I think around minute 70, they [Everton] had a little reaction and Goodison Park woke up.
"We were under a bit of pressure with a couple of corners and couple of crosses in dangerous positions. But apart from that we had the ball, we moved the ball, we were very confident with the ball and created a lot.
"The goals were phenomenal, the Mata shot was a fantastic action. Amazing save by the 'keeper on the floor with the left hand [against Lingard], a few crosses in the face of the goal. I think we played really well.
"Maybe my critics will say I performed today"
Mourinho praised his side for managing to control the game even in spite of missing top goalscorer Romelu Lukaku and having to adapt their approach in the Belgian's absence and suggested the Red Devils' display will quell recent criticisms of him as a manager.
"I think even the first half, after 10 or 15 minutes, the team was in control," the Portuguese boss continued.
"We found a way to play without a player like Lukaku, like Zlatan [Ibrahimović], with more dynamic and more freedom.
"We thought it was important to have a third midfield player. Tired people, not many players to rotate, we could anticipate that Sam was going to make a lot of changes because his squad now has lots of options so he made seven changes.
"We knew that at least an extra third midfield player would give us a little more consistency in the middle. I think the performance was really good.
"Maybe I'm lucky this time and the kings of the rock 'n' roll who said I was underperforming last match will say I have performed."