The Manchester United striker opened the scoring in the 16th minute and Luciano Narsingh added a second in stoppage time as the Dutch registered a morale-boosting victory following their poor UEFA EURO 2012 showing.
The hosts were made to fight all the way in a keenly contested Group D opener, but got the job done to hand Louis van Gaal a win in his first competitive outing following his return to the national team for a second spell as coach.
Turkey posed a threat to the Dutch goal from the very first whistle, and inside a minute had forced a corner from which Omar Toprak flashed a header just wide.
The visitors continued to press and in the fifth minute Emre Belozoglu's low drive was charged down by Johnny Heitinga.
Toprak was again in the thick of the action from another corner in the 14th minute but this time directed his header straight at Tim Krul in the Holland goal.
Given all of their early pressure the Turks will have been frustrated to fall behind against the run of play in the 16th minute.
United new boy Van Persie has started the new season like a train for the Old Trafford club with four goals in three league games, and he transferred that form to the international stage tonight with his 30th goal for the Oranje.
Van Persie completed his hat-trick against Southampton last weekend with a header from a corner, and repeated the trick tonight as he nodded home Wesley Sneijder's set-piece.
Sneijder stung the palms of Tolga Zengin in the 23rd minute as the hosts looked to doubled their lead, but Turkey fired a warning of their threat within a minute as Arda Turan twice fired just wide.
And the Dutch had a lucky escape in the 40th minute when Tunay Torun's free-kick was met by the head of Umut Bulut but the ball came back off the crossbar.
Turkey continued to press after the break and in the 57th minute Hamit Altintop's powerful effort from 25 yards produced a superb save from Krul.
Leroy Fer eased the pressure on the Dutch goal with a hopeful effort in the 62nd minute that was always rising, but within three minutes Turkey were on the attack again, Sercan Sararer heading just over from six yards.
Mehmet Topal also went close for the visitors in what time remained, but try as they might the equaliser just would not come.
And that allowed the Dutch to add a rather flattering gloss to the scoreline in the third minute of injury time as Narsingh picked the ball up on the edge of the Turkey area and netted with a cute lofted finish.
There was still time for the hosts to threaten a third, but Van Persie blazed over after connecting with Sneijder's centre.