Everton went ahead through Bernard’s shot, but two goals from Bruno Fernandes ensured United were ahead by halftime.
Edinson Cavani’s first goal for United wrapped up the win in stoppage time to provide some much needed respite for manager Ole Gunnar Solskjaer.
This was the visitors’ third consecutive away win in the Premier League in a season that has seen Solskjaer’s side lose three times and draw once at home.
The win pushed United up to 13th in the Premier League, six points behind leaders Southampton.
United’s Norwegian manager struck a combative note in his post-match television interview, complaining about having to play early on Saturday afternoon, given the game against Basaksehir in Istanbul, Turkey had been on Wednesday.
“We were set up to fail, Solskjaer told BT Sport. “The kickoff time set us up to fail. We have been to Turkey, played loads of games this season already, we got back Thursday morning and we are playing Saturday lunchtime, it’s an absolute shambles.
“The authorities set us up to fail, who is responsible? We’ve had enough of that. Players this season, in these times, a pandemic, mentally and physically it’s draining. Let us play on a Sunday, there’s an international break after this, it’s a joke.
“The problem was that after we scored we were not able to defend well, and they took advantage,” Ancelotti told BT Sport. “They were able to score easily. We said before the game we had to defend better. We were slow at the back, we have to improve.
“I hope that after the international break we will back in a different shape. It is not only a problem of the defenders, it is all of the team.”
Everton forward Richarlison was sent off in the draw against Liverpool and subsequently had to serve a three-match ban and Everton has missed the talented Brazilian.
After the upcoming international break, United plays West Bromwich Albion on November 21, while Everton is away at Fulham.