The Dutch lost their opening Group A game to Czech Republic and looked set to suffer a further setback when they fell behind to a first-half header from Kazakhstan's Renat Abdulin in Amsterdam on Friday.
However, substitute Klaas-Jan Huntelaar equalised just after the hour mark and late goals from Ibrahim Afellay and Robin van Persie ensured Netherlands avoided an upset.
Hiddink insists that first win of his second spell as national coach was never in doubt and he expects Iceland, who have won each of their opening two qualifiers, to play a more expansive game.
"I didn't have the feeling we would lose points," said Hiddink.
"During half-time we were planning Huntelaar's substitution. It was good that the fans backed us after he came on.
"I have confidence we can win the Iceland match. There will be more space to play than [against Kazakhstan]."
Iceland claimed a 3-0 victory over Turkey in their opening qualifier and followed up that success on Friday, beating Latvia by the same scoreline in Riga.
They are one of two sides in Group A with maximum points, together with Czech Republic, and are likely to be full of confidence as they aim to reach the finals of a European Championship for the first time.
Hiddink will hope to have Afellay at his disposal after the Olympiacos attacker enjoyed an impressive return to international football against Kazakhstan.
Having been handed a starting role by his country for the first time in more than two years, Afellay set up Huntelaar's leveller before scoring himself.
His participation in Monday’s match seemed in doubt following a reckless challenge from Baurzhan Dzholchiev in the second half, which saw the Kazakhstan player sent off.
However, the 28-year-old has declared himself fit and ready to play in Reykjavik.
"My foot is thick, but Monday against Iceland I can play," Afellay is quoted as saying by De Telegraaf.
"We have done well. Kazakhstan had the bus parked in their own penalty area but eventually we found a hole. Fortunately, I was able to contribute."
Netherlands ran out 2-1 winners on their last visit to Iceland, in June 2009.
