Anthony Martial and Jesse Lingard's fine second-half strikes delivered a first win in five for United.
Following a dull first 45, Martial, playing up front in the absence of injured duo Romelu Lukaku and Zlatan Ibrahimovic, curled home a 57th-minute opener before Lingard smashed in his seventh goal in nine games nine minutes from time.
Afterwards, United boss Jose Mourinho declared: “The boys deserved it. I kept saying that our draws were not bad performances. Our draws had situations which made it more difficult for us and we made mistakes ourselves, especially in the matches against Leicester and Burnley. But the players was top class and on top of it we played very well. It didn't look a performance of tired boys or the worst possible calendar that you gave us. It looked a fresh performance.
“Everton had a little bit (of control) in the first half and had a reaction in the second half for five or eight minutes, but we were always in control. We had the ball, we moved the ball, we changed our profile because we didn't have Romelu Lukaku, we had to try to play in a different way, and I am really pleased with the points. But even without the points, I would be proud of what the boys did."
Mourinho was delighted with the approach of his players.
“The boys were fantastic - the attitude, the commitment, the desire, the professionalism, the pride. I thought they were absolutely fantastic and on top of that, they produced not just a professional performance but I think a high quality performance too. The boys were fantastic in the way they controlled the game, controlled an amazing stadium with a very strong atmosphere which supports incredibly well the home team. We managed to calm them and to be in control and on top of that the goals are good goals, so I think a fantastic three points. We had good penetration on the sides, we had good crosses and I thought we played very well."