Villa had gone close through Jack Grealish and Trezeguet before the away side took the lead, Bruno Fernandes netting a penalty after a contentious decision.
Mason Greenwood then smashed in a second just before the break and Paul Pogba curled home a third to put United in a commanding position.
Villa mounted barely any response at all in the second half and slip to 19th after Bournemouth drew earlier in the day.
Here are five things we learned from the match at Villa Park.
Absurdities and poor decisions
It’s a close call in these Villa games: Was the worse decision Sheffield United’s ‘goal’ which wasn’t given as the goal-line technology couldn’t see it? Or was it the penalty call here for United and Bruno Fernandes?
Fernandes produced a great piece of skill to spin on the ball and protect it from the defender on the edge of the box, but that’s as much as happened.
Ezri Konsa planted his foot to make a block, rather than a tackle, a full step before there would be any contact with Fernandes. And it was the Portuguese man’s spin which took him further, onto Konsa, actually stepping on his leg and very definitely initiating, not receiving, the contact.
In real time, with bodies moving different directions, perhaps it’s understandable that a foul and penalty was initially given. But that’s precisely why we have the Video Assistant now, to help point out when mistakes have been made.
It was, clearly and obviously, not a penalty. To everyone in the ground and to everyone watching on from further afield. Except the referee, and his VAR, of course.
Villa’s summer task
If they go down, Villa will probably be expecting to have to sell a few players – Grealish will obviously be one.
Another may be Tyrone Mings, though on certain recent displays that’s not something to be overly distraught about.
But some others have shown they are Premier League calibre. Konsa had to wait for his chance, but has been a solid performer. Trezeguet is another who has shown flashes of ability, though not consistently enough.
But Douglas Luiz is a legitimate talent, a carrier of the ball, a winner of possession and an organiser, a leader, in the middle of the pitch.
The Brazilian berated his team-mates for not countering quickly, demanded more movement of them, asked for more speed in the play – and technically he was mostly excellent. He’ll be tough to keep around in the second tier.
Headlines for Greenwood, but central duo run the show
Greenwood is unstoppable in full flow, capable of going either side, shooting with either foot, scoring from close in or long-range.
He’ll probably get headlines again after this fixture, after netting a fourth goal in his last three games.
But United’s real strength, their control of the game and their exploitation of the gaps Villa left, came once again from the more central duo of Pogba and Fernandes.
The Frenchman pulled the strings from deep, then pushed on once his team were in the ascendency and scored a tremendous goal. His new team-mate netted the opener, set up Pogba’s goal and generally found space between the lines at every turn, always giving United a chance to play forwards, look to attack and get runners around him.
Champions League push
One point behind Leicester with four games to go – that’s the situation now for United.
It looks increasingly as though a top-four spot, and a Champions League guaranteed spot with it, could come down to a final-day shoot-out between the two sides.
United very much have the form and confidence behind them, and more importantly, Ole Gunnar Solskjaer looks to have found his best XI.
In contrast to Leicester, who have had injuries, changed formation and poor results, it’s looking extremely promising for the Old Trafford side to go on and secure the place they want.
It’s the complete opposite for Villa, who dropped a spot earlier in the day after Bournemouth took a point and are now 19th in the table, four points from safety.
The goal difference took a bit of a beating here, too, though that will hardly matter if they continue failing to take any points at all.
Two goals in six games since the restart speaks volumes as to where Villa have struggled; with an attempt to tighten up at the back came a complete absence of attacking thrust.
And even that defensive resolve was lost early on here, with Villa’s crumbling mentality as much of a concern to Dean Smith as the eventual scoreline on the night.