The Dutch are top of Group D with a maximum 18 points from six matches while Romania are third on 10.
"This was the best match under my management so far," Netherlands coach Louis van Gaal told reporters.
"We executed our game plan much better than we did on Friday [3-0 v Estonia]. We only played sloppily in the final quarter of the first half and that resulted in their sole chance of the match."
Playmaker Van der Vaart opened the scoring after 11 minutes with a well-placed shot with his right foot after good work from Jeremain Lens and Van Persie.
Arjen Robben then showed his brilliance when he beat two Romanian defenders before setting up Van Persie to double the lead with a header from a tight angle after 55 minutes.
Van Persie added another nine minutes later when he converted a penalty after Lens was fouled. In the final minute, Lens completed the rout from close range when he netted a rebound.
The Dutch started in inspired form and created two good chances before Van der Vaart, who replaced the injured Wesley Sneijder, opened the scoring.
Romania never seriously threatened the Dutch defence until minutes before the break when Daley Blind failed to clear and allowed Adrian Popa to shoot on goal though Kenneth Vermeer saved.
Van Persie's double in the second half settled matters as the Dutch managed their 14th consecutive World Cup qualifying win.
