The Dutchman needed just three minutes to remind the Gunners of what they lost when he quit the Emirates Stadium in a £24million deal in the summer.
The 29-year-old set up what proved a routine 2-1 win for United over their Barclays Premier League rivals at Old Trafford with his early goal.
Van Persie told Sky Sports: "It was a special day, it was quite a game. I think we played well.
"We had a few chances, we should have scored two or three more but in the end we're happy with the three points which is all that matters."
The 29-year-old was taunted throughout by visiting fans but he did not antagonise them further by celebrating his goal.
He said: "I think it speaks for itself. I played there eight years and had a fantastic time there.
"I have respect for the fans, the players, the manager and the whole club."