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.
"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 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."
