Roberto Martinez praised his side for coming out of a potentially gruelling encounter against a fresher Manchester United with all three points.
The Blues' busy week continued with Easter Sunday's game against the current league champions, who themselves had not had a fixture for 11 days.
Leighton Baines' penalty and Kevin Mirallas' cool finish provided first-half damage from which the Red Devils were unable to recover, leaving Martinez beaming with pride.
He said: "It was a very satisfying performance, especially being the third game in eight days.
"I thought it was going to be a really demanding game, so to be able to be so good in what we were trying to do was pleasing.
"Being 2-0 up was a risky moment where you expect United to throw everything at you. But to keep a clean sheet from that point on after what happened on Wednesday, I was very proud.
"Tim Howard made a world-class save in the 86th minute and for all the quality Manchester United had on the pitch, that speaks volumes of our defensive display."
Martinez made two changes to the side that lost against Crystal Palace on Wednesday, recalling Steven Naismith and James McCarthy in place of Aiden McGeady and Gerard Deulofeu.
And the Spaniard believes being able to rotate his squad in recent weeks has been a timely boost.
Everton moved back to within a point of fourth-placed Arsenal, who had earlier won at Hull City.
And the Blues boss reflected: "We had to be clever in using our energy right. We've been able to use the squad for the last six or seven weeks and that's probably been the difference.
"It's an important balance between having players that are fresh and those that have been contributing. We have the right balance with the squad going into the final games.
"That performance was dynamic and full of energy. We looked electrifying on the counter-attack and a very exciting team to watch.
"We had to be patient and pick our moments, and, when we did, I think we were terrific."
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