Hiddink's side lost their first Group A clash to the Czech Republic last month and trailed 1-0 at the hour-mark at home to 127th-ranked Kazakhstan.
Klaas-Jan Huntelaar's header restored parity in the 62nd minute, though, and the visitors had their hopes significantly dented by Baurzhan Dzholchiev's red card just after.
It still took until the 82nd minute for the Netherlands to hit the lead, Ibrahim Afellay's deflected strike relieving the crowd in Amsterdam.
And Robin van Persie sealed the nervy win with an 89th-minute penalty, but Hiddink was not worried - maintaining he always had faith in his side.
"We can be satisfied," Hiddink said.
"In the first half we put them under pressure. And it is an unwritten law that if you don't score then you will score in the last 20 minutes.
"It was nice to see Huntelaar scoring with a beautiful, classic header.
"After the equaliser it was a matter of time until we scored our second goal. You could feel that."
Netherlands travel to Iceland for another Group A match on Monday.
