Huntelaar began the rout in the fourth minute after a fine move involving Wesley Sneijder and Rafael van der Vaart before Sneijder set up Afellay to double the lead.
Huntelaar and Afellay, only starting because of injuries to Robin van Persie and Arjen Robben, added second goals before the hour mark, with Andreas Granqvist pulling one back for the Swedes with around 20 minutes to go.
The only real down side for the Dutch was an injury to Dirk Kuyt, who hurt his right ankle when he landed unfortunately after jumping for the ball. The Liverpool forward was taken to hospital for tests.
The result left the Dutch top in Group E with a perfect 12 points from four matches. Hungary are second with nine, three ahead of Sweden and Moldova, who lost 1-0 to the Dutch on Friday.
"This was a great match from my team with some good football and we scored the goals we didn't get on Friday at Moldova," Dutch coach Bert van Marwijk told reporters.
"In the final phase we came under some pressure but that has to do with tiredness, after our second match in five days."
The visitors had just one chance to fight back before the game was won when Ola Toivonen broke through only for his lob to miss the target by a fraction.
The Dutch dominated with Van der Vaart excelling in the role of holding midfielder in place of Nigel de Jong, dropped after his rough tackle in a Premier League match.
"With this midfield there is so much more football in my team," Van Marwijk said.
"This is an important day when you prove that you can play like this against such an opponent."
