Depay scored a double in a man-of-the-match performance against Lithuania as the Dutch escaped with a narrow 3-2 win to advance to 10 points from four games in the qualifying group.
Depay had been level on 50 goals with Robin van Persie after scoring twice against Malta in June to tie the record, but on Thursday, he missed out on a chance to set a new mark as he and his teammates had an off-colour performance against Poland in a 1-1 draw in Rotterdam.
But on Sunday, Depay took all of 11 minutes to set a new record and then won the game for the Dutch with a powerful header after Lithuania had fought back from two down to be 2-2 with 30 minutes to play.
"I'm super proud and very glad I got past Robin. I thanked everyone in the dressing room," he told Dutch NOS television.
“I also want to thank old teammates like Klaas-Jan Huntelaar and Arjen Robben, for example. They inspired me. The same goes for Patrick Kluivert. It was because of him that I wanted to reach the Dutch national team."
Depay, who now plays club football in Brazil with Corinthians, also had a dig at critics who raised concerns about his consistency.
"People often say, 'What are we supposed to do with our striker position?' But we actually have a striker who scores a lot of goals," he said of himself.
"I try to let my feet do the talking; they're not going to get rid of me just yet."