The Manchester United star netted twice to take his tally for the Oranje to 34 goals in 74 appearances and help the hosts maintain their perfect qualifying record.
Rafael van der Vaart gifted the Dutch an early lead with a low shot form the edge of the area, before van Persie made it two after the break with a good header from Arjen Robben's cross. The Manchester United man doubled his personal tally halfway through the second half when he converted a spot kick, with Jeremain Lens making it four in the closing minutes of the game.
The home side started the match with attacking intentions, and came close to opening the scoring early on on a number of occasions. Kevin Strootman first saw his shot saved by Costel Pantilimon, though, before van Persie aimed too high from close range after a superb cross from Lens.
Netherlands did grab the lead after 12 minutes, after yet again some good work from Lens. The PSV winger reached Van Persie on the edge of the box with a low cross from the right, who then laid the ball off for Van der Vaart. The Hamburg star didn't hesitate and beat Pantilimon with a right-footed shot from 18 yards out.
Romania got back into the match after Oranje's early opener, and almost restored parity after 38 minutes of play. Right winger Adrian Popa tried his luck with a low shot from a narrow angle, but Kenneth Vermeer pulled off a superb save to keep his side in the lead.
The Dutch got a good chance to double their lead shortly after the break following some sloppy defending from Florin Gardos. The Steaua Bucharest defender failed to clear a cross from Strootman, but Van Persie's shot lacked accuracy, allowing Pantilimon to make an easy save.
The Oranje scored their second goal of the game shortly after, though. Robben reached van Persie with a perfect cross after going past his marker down the left, and the forward beat the Romanian goalkeeper with a subtle header.
Lens continued to cause the guests all kinds of trouble with his dribbles down the right, and the referee had no other choice but to award Netherlands a spot kick after Gardos fouled the PSV attacker. Van Persie stepped up to take it and coolly slotted home to surpass Johan Cruyff's Netherlands goal tally and make it 3-0 with his 34th international goal.
Things deteriorated even more for the away side in the closing stages of the game when Lens added his name to the score sheet. Pantilimon failed to hold on to Adam Maher's powerful shot, and the PSV star tapped home from close range to pour even more salt in Romania's wounds.
The Netherlands sits atop of Group D with 18 points from six games, while Romania is in third with 10 points.