The prolific Dutchman was taunted throughout by visiting fans but reminded them of his talents in the opening moments in a Barclays Premier League contest United dominated from the outset.
Wayne Rooney missed United's fourth penalty of the season but Patrice Evra added a second and Arsenal's misery was compounded by the sending off Jack Wilshere before Santi Cazorla hit an injury-time consolation.
England midfielder Wilshere had been making only his second appearance for the Gunners after a 14-month injury lay-off.
United were 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 fans made clear from the moment his name was first read out what they now thought of their former hero.
Van Persie's eight year stint in north London culminated in last season's magnificent 37-goal campaign but he was cheered when he slipped in the opening minute.
But the 29-year-old needed little time to remind the Gunners of what they lost when he left the Emirates Stadium in a £24million move over the summer.
Arsenal's defensive frailties were again in evidence as United swept forward and Antonio Valencia bypassed Andre Santos by releasing Rafael down the right with a deft backheel.
The Brazilian whipped in an awkward low cross which caught Thomas Vermaelen off balance and his attempted clearance rolled straight to Van Persie, who fired past Vito Mannone from inside the box.
It was his 10th goal for United in 13 games but he avoided antagonising Arsenal supporters further by deciding not to celebrate.
Conceding so early may have led to some anxiety in the Arsenal camp after their 8-2 capitulation in the corresponding fixture last season.
United may not have threatened a repeat of that scoreline but they continued to control the game and the best response the visitors could initially muster was a wayward long-range drive from Santos.
That was a rare moment of opportunity for Santos, who found himself under considerable pressure at left-back.
United may have seemed content to build a patient game but attacking Santos' flank seemed a fruitful avenue for the hosts, with Valencia troubling the Brazilian at every opportunity.
Van Persie went close again as he raced onto a defence-slitting pass by Rooney but Mannone saved well.
Arsenal did show some positive intent with Aaron Ramsey, the only starting member of their side who played in last year's thrashing, reaching the byline but David de Gea pushed away his cross.
Valencia predictably beat Santos to cross and Michael Carrick clipped the ball to Rooney after Bacary Sagna had half-cleared.
Rooney steadied himself to shoot but Mannone produced another good save and Van Persie headed straight at the goalkeeper after the ball was worked back in.
United could have doubled their lead on the stroke of half-time after Cazorla handled an Ashley Young cross at point-blank range just inside the box.
The Spaniard felt the award was harsh and he could argue he was protecting his face but it did not matter as Rooney dragged the resulting spot-kick wide.
Another goal might have been the least United deserved for their first half superiority but it was a reminder of their early season deficiencies from 12 yards.
Questions will certainly be asked as to why the in-form Van Persie did not take the responsibility.
United were close to doubling their lead again after another Vermaelen error early in the second half allowed Van Persie to break but Valencia could not turn in his low ball.
Carrick then shot wide from distance after a shot by Rafael was half-cleared as far as the England midfielder.
Arsenal continued to lack a spark but Olivier Giroud almost provided one after a neat touch beat Rio Ferdinand and gave him a shooting chance but he could only hit the side-netting from a tight angle.
Van Persie was booked after a late challenge on Sagna but was back in more familiar position just after the hour as he was picked out by a fine cross by Ashley Young, but Mannone got a vital hand to his low shot.
Arsenal could not hold out much longer and from a short corner routine Rooney crossed for Evra and the Frenchman planted a firm header inside the post.
The Gunners' agonies grew as Wilshere, booked in the first half and fortunate to escape a second yellow card for a bad tackle on Van Persie, was penalised for one bad tackle too many, this time on Evra, and saw red.
Van Persie and substitute Anderson both thought they had added a third for United but were both correctly denied by an offside flag.
United played out the closing moments with little alarm until Cazorla netted a fine consolation from the edge of the box with what proved the last kick of the game. Click to signup for FREE news updates, latest information and hottest gists everyday
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