Wesley Sneijder set up Van der Vaart for a shot from 12 metres that goalkeeper Gabor Kiraly could only tip into the left corner.
Ibrahim Afellay should have doubled the lead in the 32nd minute but the Barcelona striker made no mistake with another chance on the stroke of half-time.
Robin van Persie set up Dirk Kuyt for the third before the Arsenal marksman grabbed his 20th goal in 53 games for the World Cup runners-up in the 62nd minute.
The Dutch now have 15 points from five games, six in front of second-placed Hungary. Sweden are third with six points from three matches.
"Our style is to keep the ball as much as we can and pass it around a lot and today we did a great job of that," said Dutch coach Bert van Marwijk.
"Hungary did not have the confidence to put us under pressure. We sometimes got careless but before the home team found their rhythm we scored the second."
The visitors were without several players on Friday but the performance of the team showed how much strength in depth they possess.
Captain Mark van Bommel missed out with a thigh injury, striker Klaas-Jan Huntelaar is recovering from a knee problem and winger Arjen Robben was sidelined with a groin strain.
First-choice goalkeeper Maarten Stekelenburg is also out for the rest of the season with a broken right thumb.
"The Dutch are one of the world's best teams and they showed that tonight," said Hungary coach Sandor Egervari. "We did not perform well and did not prove up to the task."
