The Dutchman, who joined United from the Gunners in the summer, gave the hosts the perfect start in the third minute when he lashed home after Thomas Vermaelen made a hash of a simple clearance inside the box.
United were dominant against a subdued Arsenal and had the chance to double their lead just before the break when Santi Cazorla gave away a penalty for handball in the box – but Wayne Rooney missed the spot-kick.
Sir Alex Ferguson’s men finally doubled their advantage in the 67th minute when Patrice Evra headed home.
Matters then got worse for the visitors when Jack Wilshere was sent off for a second bookable offence, before Cazorla netted a late consolation.
“It was a special day but in the end it was about the game,” Van Persie told Sky Sports. “I think we played well, we were a bit sloppy with chances and should have scored a few more but in the end I’m happy with the three points.”
Van Persie said he chose not to celebrate his goal out of respect for his former employers. “I think it speaks for itself,” he said.
“I played for eight years and had a fantastic time there. I respect the fans, the players, the manager and the whole club.
“It’s the first time ever that I’ve played against my former club because I only have three. It was a special day but in the end it’s about the game and we won it.”
The Dutchman also insisted he was not aware of any of the chants aimed his way by the fans of his former club. He added: “I honestly didn’t hear them. They are great fans and I do respect them a lot.”
The win lifts Manchester United above Chelsea into first place in the Premier League table and Rooney admitted his delight at seeing his side leapfrog their title rivals.
“We knew before the game if we won we’d go top of the league and it’s important for us,” he said.
“After the first day of the season and dropping three points we’ve done well. We’ve grinded results out and we’ve played some good football.”
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