The Dutchman scored the only goal of an absorbing encounter that saw the Gunners' lead at the top of the table reduced to two points, while United now trail Arsene Wenger's side by just five despite their own indifferent form at the start of the new season.
It was Van Persie's third goal in as many games against his former club but the forward is adamant that victory was a result of magnificent collective effort, rather than his own individual striking prowess."It was a massive win," he told MUTV. "I always like to think positively but, if you think negatively for one second, we could have been 11 points behind, which would have been dramatic.
"I don't think you can beat a team like that with just a couple of individuals playing well. You need to be strong as a team. That is what we did.
"Everyone closed everyone down. If you look at Patrice Evra, every header or 50-50 challenge, he went for it. The back four did it. Even the front players did it. That makes a difference."
On the goal itself, Van Persie added: "It was a good corner from Wazza [Wayne Rooney]. I headed it but then it took a touch off my shoulder, then it went in.
"It didn't really matter whether it went in off my head or my shoulder. I am very happy with that head-shoulder goal."