Oranje were struggling to break down the 10 men of the visiting minnows until Afellay struck with eight minutes remaining, and the Manchester United forward was full of praise for the ex-Barcelona man.
Van Persie told Goal.com: "It was a double liberation - not only for the team, but for him. It was beautiful.
"I know how hard he's had it. I've been in touch with him in Barcelona, I know where he's coming from. If he scores the winning goal, I'm very happy for him.
"He's come a long way and is now back at the top."
The appearance was Afellay's first for the national side for two years.