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.
Patrice Evra added the second after Wayne Rooney missed a penalty while the Gunners' misery was compounded by the sending off of Jack Wilshere, although Santi Cazorla hit a late consolation.
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."
Van Persie spent eight years with the north London club, culminating in last season's superb 37-goal campaign.
He has carried that form with him to United and his latest effort took his tally this season to 10 in 13 games.
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."
United defender Rio Ferdinand said on MUTV: "He showed a bit more class than probably their fans did to him, but it is banter from their fans and he celebrated in the right way, I think."