The £24million striker took just three minutes to score against the club he left in the summer, and the hosts could even afford the luxury of a missed Wayne Rooney penalty as Patrice Evra's second (67) and a red card for Jack Wilshere made it another dismal day in Manchester for Arsene Wenger despite Santi Cazorla's late reply (90).
The scoreline may have lacked the ruthlessness of last season's 8-2, but with 10 games gone Arsenal are worse off than in any previous season under Wenger - nine points behind United, who moved a point clear at the top thanks to Swansea's draw with Chelsea and Manchester City's stalemate at West Ham.
It took until injury-time for the visitors to bring a first save out of David De Gea, a lack of bite which was brought into painful focus by the menace of their former captain.
Van Persie had scored nine in 12 appearances for United so he scarcely needed the invitation to shoot provided by Thomas Vermaelen, whose miscued clearance from Rafael da Silva's innocuous cross fell perfectly for his former team-mate to bobble a 20-yard shot beyond Vito Mannone.
The goal left Arsenal chasing for the eighth time in 11 games, and an obvious lack of confidence in possession allowed United to wait for a mistake, Aaron Ramsey's dithering on halfway inviting a break which ended with Mannone keeping out Van Persie at his near post.
And when the Gunners defence was slow to follow out Bacary Sagna's headed clearance Michael Carrick returned the ball for Wayne Rooney, whose left-footed drive brought a more convincing stop from the Italian.
United should have put it to bed either side of half-time, but Rooney dragged his penalty wide after Cazorla had handled in the box and Antonio Valencia miskicked in front of goal after another Vermaelen blunder put Van Persie in.
Arsenal briefly threatened to cash in, Olivier Giroud spinning onto Cazorla's pass and clipping the outside of the near post, but only a fingertip stop from Mannone denied Van Persie a second and when the resulting corner was played short Rooney's cross was headed in by Evra.
Any realistic chance of a comeback disappeared down the tunnel with Wilshere - given a second booking for catching Evra on the overstretch - and Cazorla's fine injury-time goal was a barely relevant footnote.
Before Cazorla's late consolation, Van Persie and substitute Anderson both thought they had added a third for United but were both correctly denied by an offside flag.
While Cazorla's goal had given Arsenal fans something to cheer, United had been superior in almost every department against a side they fought out a bitter rivalry with in the last decade.
The sight of Van Persie in their ranks will have hurt, and the Arsenal supporters had made it clear from the moment his name was first read out what they now thought of their former hero.
And with England midfielder Wilshere sent off on only his second appearance for the Gunners in the last 17 months, it had been a journey north to forget.
| Manchester United | Team Statistics | Arsenal |
| 2 | Goals | 1 |
| 1 | 1st Half Goals | 0 |
| 6 | Shots on Target | 2 |
| 5 | Shots off Target | 3 |
| 2 | Blocked Shots | 2 |
| 6 | Corners | 1 |
| 15 | Fouls | 15 |
| 5 | Offsides | 1 |
| 5 | Yellow Cards | 2 |
| 0 | Red Cards | 1 |
| 86.5 | Passing Success | 87.9 |
| 22 | Tackles | 10 |
| 77.3 | Tackles Success | 90 |
| 47.9 | Possession | 52.1 |
| 53.5 | Territorial Advantage | 46.5 |
| 533 | Total Passes | 593 |
| 27 | Total Crosses | 16 |
| 133 | Lost Balls | 137 |
| 61 | Recoveries | 57 |
| 44.6 | 1st Half Poss. | 55.4 |
| 50.8 | 2nd Half Poss. | 49.2 |
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