Manchester City's 3-1 loss at Tottenham Hotspur a day earlier had handed United a chance to regain the title and Alex Ferguson's men needed no second invitation, swamping Villa to claim the championship with four games to spare.
Van Persie, United's number 20, was the man who brought United their 20th top-flight crown, netting inside 90 seconds and then scoring a breath-taking volley before completing his hat-trick 12 minutes before half-time.
"I am very happy, but it is weird. I had to wait so long for my first title. It is a great feeling," van Persie told Sky Sports.
"This is our 20th title. It is deserved."
With 13 Premier League titles, United manager Ferguson and veteran midfielder Ryan Giggs, creator of two of van Persie's goals, have now each won as many English league crowns as Arsenal.
Eternal rivals Liverpool, meanwhile, now trail United by two championships on the all-time honours board.
"I'm delighted for all the players, for myself, the staff and the supporters," said Ferguson.
"You can go on and on about losing the title (last season), but at the end of the day, our consistency for the last 20 years is unbelievable.
"The focus of the team was good, they focused on the challenge of City and came up trumps."
Wayne Rooney, who was making his 400th appearance for United, said the achievement partially atoned for the pain of losing last year's title to City on the season's final day.
"When you lose the title, it is hard to take," he said.
"It wasn't a nice feeling last time. We have all dug in deep and done fantastic to put ourselves in this position.
"You can never take anything for granted in football and thankfully it is now done."
Villa never threatened to poop the party and remain under threat from third-bottom Wigan Athletic, who could suck Paul Lambert's side into the relegation zone if they win their game in hand.
"I am proud that my lads kept on going and credit to them, especially against the best team in the country," said the Villa manager.
The evening's outcome was never in doubt from the moment, just one minute and 23 seconds into the game, when van Persie put United in front.
Rafael da Silva's delivery from the right appeared overhit, but Giggs rescued it by volleying a cushioned cross across goal for the Dutchman to tap in from barely a yard.
A chant of 'Championey!' rang out from Old Trafford's Stretford End as United continued to press, Rafael hitting the post with a crisp strike from 20 yards.
Villa threatened to spoil things when Christian Benteke side-footed over from Andreas Weimann's pass, only for van Persie to double United's lead with a strike to rival any goal scored in Europe this season.
Rooney floated a 40-yard pass behind the Villa defence and van Persie met the ball first-time with a technically immaculate volley from outside the box that rocketed past goalkeeper Brad Guzan and into the net.
"It was a great ball from Wayne, so the only thing I had to do was guide it right and hit it properly and it went in great, but more important was the result," said van Persie.
Ferguson agreed, calling it "the goal of the century".
"It was marvellous -- the technique with his head down, over the ball, and just perfect timing," said the Scot. "It was a magnificent strike."
On a night rich with symmetry, van Persie's third goal arrived in the 33rd minute.
Shinji Kagawa freed Giggs, who unselfishly squared to van Persie, and the former Arsenal striker neatly side-stepped Guzan before lifting the ball into the roof of the net.
With 24 goals, United's £24 million ($37 million, 28 million euros) man now leads Luis Suarez by a goal in the top scorers' chart, to further blacken the Liverpool striker's mood after he was charged by the Football Association for biting Chelsea's Branislav Ivanovic on Sunday.
Van Persie further illustrated his value by heading off the line from Weimann early in the second half, while David de Gea saved smartly from Benteke and Karim El Ahmadi.
Kagawa spurned a glorious chance to make it 4-0 when he blazed over the bar, but by then the match, like the title race, had long been decided.
Mumbai Roundup: 9 incidents that took place this week
Photos: Ajay Devgn, Parineeti, Tabu at 'Golmaal Again' trailer launch
Photos: Dipika Pallikal Karthik oozes oomph in bikinis and sarees
Photos: Kareena Kapoor Khan's grand birthday bash
Photos: 'Dangal' girls Sanya Malhotra, Fatima Sana Shaikh's dinner outing