Villa, desperate for damage limitation in their relegation battle, did a better job of containing United in the second half and Van Persie was called on to demonstrate his worth at the other end of the field with a headed clearance off the line.
Kagawa missed a chance to give United a fourth, inexplicably firing high and wide, but that will be forgotten as the party gets into full swing.
Television pictures from the club’s in-house MUTV station showed the players spraying champagne around the dressing room, and jumping up and down on the benches.
While the celebrations were likely to carry on into the night, United’s players will not get their hands on the trophy for another three weeks, as it will not be presented until their final home match of the season against Swansea City on May 12.
United, who have 84 points to City’s 68, with their neighbors having played one game fewer, head to Arsenal for their next match on Sunday, where they can continue the party in front of Van Persie’s former teammates.
Asked what he thought about going back to the Emirates as a champion with United, Van Persie replied: “Let us enjoy tonight first.”
It was fitting that the goals came from the man whose hot form has driven United’s season.
His arrival in the summer from Arsenal was a signal that Ferguson would be true to his vow that his side would never again miss out because they had not scored enough goals.
Van Persie’s hat-trick against a young Aston Villa team, who remain a perilous three points above the relegation zone with some damage to their goal-difference, took him above Liverpool’s Luis Suarez on top of the scoring charts.
The debate will rage over where this United team fits in among Ferguson’s great sides of the past, with this crop sometimes criticized for not living up to the likes of the 1993-1994 double-winners or the 1998-1999 treble winners.
However, there will be few that would argue about Van Persie’s place among the Old Trafford greats.