Wayne Rooney bagged a first half brace to overcome the early deficit before Juan Mata opened his United account, then another fine cameo from Adnan Januzaj created a fourth for Javier Hernandez.
The small matter of the Moyes Out banner was dealt with well by all at the ground - Moyes himself came out early, well before the team, and when the banner flew overhead it was greeted with a chorus of boos before several chants backing the manager and attacking the banner.
The good mood did not last too long, however, as Rafael launched into a pair of reckless challenges, the second of which earned him a yellow card and from which Ashley Westwood curled home an excellent free-kick, to nerves around Old Trafford.
But United weren't behind for long. A fine dinked cross from Shinji Kagawa found Wayne Rooney at the back post to nod past Brad Guzan and equalise for United in a game that was looking increasingly open and end-to-end. Yet the excitement would die down there for a while, as most of the rest of the half was taken up by a midfield battle and neither side getting a grip on the game.
Yet just as half-time was arriving, Juan Mata showed some good footwork to bamboozle Leandro Bacuna, who brought the Spaniard down for a clear penalty. Rooney stepped up to take it, and duly smashed it home to offer some small vindication for Moyes.
Half-time saw Moyes withdraw Rafael, presumably fearing a red card, but United did not suffer without him as they have done often this season. It was not too long before they had a third, courtesy of Juan Mata, who got onto a loose ball in the area as the Villa defence struggled to deal with the physical presence of Marouane Fellaini, and fired past Guzan to put United in a more commanding lead.
Adnan Januzaj's introduction was a most welcome one, and he showed some fine skills before capping it off with a quite magnificent assist, latching on to Fellaini's through-ball, beating his marker and then steering in an undefendable cross for the lurking Javier Hernandez at the back post to make it 4-1.
So, fairly emphatic, although the chances of us pulling off a performance like this against a good side - a team such as, oh, I don't know, Bayern Munich perhaps - are unlikely if the past is anything to go by. There are undoubted signs of improvement in United's play and performances against the poorer teams in the Premier League, but they must begin to translate it to bigger games. Soon, we shall see.