Van Persie was on target with two first-half headers in the World Cup qualifier at Amsterdam Arena to draw level with the 40 international goals of Patrick Kluivert, the former striker who is now one of coach Louis van Gaal's assistants.
After heading home Arjen Robben's cross in the 43rd for his second goal of the night to tie the 10-year-old scoring record, Van Persie ran across the field and jumped into Kluivert's arms on the touchline.
"Records are made to be broken ... I'm happy for him," Kluivert said. "Every international, we work toward perfection. It is good for the Netherlands, it is good for him."
The Manchester United star, playing his 80th international, completed his hat trick in the 53rd, tapping in after Robben nodded down the ball to give the Netherlands a 5-1 lead in the Group D match.
"I thought the second was fantastic. The pass (Robben) gave was so beautiful — a floater I just had to nod in," Van Persie said. "The third was also a fantastic assist from Robben."
He was substituted after an hour to a standing ovation in Amsterdam.
Van Persie had been in doubt all week with a sore little toe and said he had only been cleared to play early Friday.
"At the last minute we decided I could play an hour," he said.