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.
"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."
"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."
