The prolific Dutchman, who joined United from Arsenal in August having scored 37 league goals for the Gunners last season, needed less than three minutes to put the hosts ahead after a mistake by Thomas Vermaelen and Patrice Evra wrapped up a comfortable win with a 67th minute header.
Santi Cazorla netted in injury time for an otherwise disappointing Arsenal, who were reduced to 10 men after the break when recently returned midfielder Jack Wilshere was sent off for a second yellow card.
Wayne Rooney also missed a penalty for United on the stroke of halftime but it never looked like proving costly. United have 24 points from 10 games and will remain on top if Chelsea (22 points) fail to win at Swansea City later on Saturday (1500 GMT). Champions Manchester City, in third place on 21 points, conclude the day's Premier League action with a testing trip to West Ham United (1730).
Arsenal lost the corresponding fixture 8-2 last season and while they never looked in danger of such a thrashing again, the final scoreline rather flattered Arsene Wenger's side.
Without Van Persie's goals they have looked toothless in the Premier League this season and Wenger's side are already falling well off the pace, having picked up 15 points from 10 games. Almost inevitably it was Van Persie who was their tormentor.
He rarely needs any help in finding the back of the net but former team mate Vermaelen provided it in the third minute when he made a hash of trying to clear a cross from Rafael and the ball fell to Van Persie who struck a first-time shot past Vito Mannone.
"A special day, in the end it was quite a game," Van Persie, who did not celebrate his goal, told Sky Sports.
"It speaks for itself (why he did not celebrate). I played eight years there and had a fantastic time. I wanted to respect the fans, the manager and the whole club."
Arsenal struggled to make any real impact and only Wilshere, making his second start since returning from a long injury lay-off, showed any real urgency in the opening period - earning himself a yellow card for a foul on Tom Cleverly.
Van Persie had another effort saved by Mannone as United looked for a second and moments before the break the hosts were awarded a penalty when Ashley Young's cross was blocked by the arm of Cazorla and referee Mike Dean pointed to the spot. Arsenal enjoyed a huge let-off though as Rooney's penalty slithered just wide of Mannone's right hand post.
Vermaelen made another terrible error just after the interval, gifting possession to Van Persie whose low cross looked inviting for Antonio Valencia but he failed to make any meaningful contact in front of goal. Evra finally gave United breathing space when he headed in from close range after 67 minutes, two minutes before Wilshere was shown a second yellow card for a clumsy foul on Evra. Cazorla gave Arsenal's fans something to cheer, curling in a superb shot with the final kick of the game.