What had been billed as a difficult afternoon for Moyes turned out to be plain-sailing as a Wayne Rooney double and goals from Juan Mata and Javier Hernandez sealed a relatively comfortable win for Moyes.
A group of disgruntled fans carried out their threat to fly a protest banner over Old Trafford.
A plane buzzed over the ground for the first 10 minutes of the match with the message 'Wrong One - Moyes Out' behind it.
Former United defender Gary Neville said the protest lacked class and most of the fans inside the stadium agreed. There were boos and songs of support for Moyes as the plane hovered above the stadium.
Moyes received a warm welcome when he took his place in the dugout and there were supportive songs for the United boss in the second half as it became clear the hosts were set for victory.
"The support inside Old Trafford has been terrific and if ever there was a show of support for their football club and for their team, it was today," the United boss said.
"Inside Old Trafford it was terrific, it really was."
Moyes said he took no notice of the plane.
"I was concentrating on the game," he said.
Perhaps the most poignant moment of the afternoon was when Moyes came out of the tunnel early and took his place on the United bench well before his players emerged.
The United manager, who has lost six home games this season, was pleased to see the response from the crowd.
"I just wanted everybody to know that I am the manager of the club and you know where I am," he said.
"I stand on the edge of the pitch every week. That's my job."
It looked like being yet another bad day at the office for Moyes when Ashley Westwood bent a free-kick over the wall and past goalkeeper David de Gea with just 11 minutes gone.
Rooney equalised seven minutes later though before he converted a penalty in first-half injury time following a foul by Leandro Bacuna on Mata.
Mata scored his first goal for the club to make it 3-1 and Adnan Januzaj set up his fellow substitute Hernandez for the fourth at the death.
"We didn't get off to a great start after 10 or 15 minutes but I thought we did a good job today," Moyes said.
"I thought the players played well, and did a lot of good things.
"We scored some good goals which we have not done in a lot of games here.
"I thought the fourth goal was (an) especially good goal."
Moyes was pleased to see club record signing Mata finally score his first United goal since his £37.5million transfer from Chelsea.
"Juan has deserved it. His play has been very good," Moyes said. "He has made a difference to the team."
The only downside for Moyes was a thigh injury to right-back Rafael, who had to come off at half-time.
Moyes, who was without Chris Smalling, Jonny Evans and Rio Ferdinand, could do without more injuries ahead of Tuesday's Champions League game against Bayern Munich.
"Rafael has an injury and we will need to check it out," the Scot said.
"We had to juggle it around a bit as Antonio Valencia couldn't play. He had a bit of tendonitis in his knee."
Villa beat Chelsea two weeks ago, and manager Paul Lambert felt his team missed another chance to pull off an upset on Saturday following a strong start.
"There was never three goals between us," Lambert said.
"We started the game great, and Westwood scored a great free-kick.
"We were comfortable at 1-0 and Manchester United were not creating too much."
Lambert's side would have had a better chance of victory had Christian Benteke not fluffed three good chances to score, but the Villa boss refused to blame the big Belgian.
"I can't be too critical of Christian because he has scored some vital goals in the last 18 months and will continue to do so," Lambert said.