Marc Wilmots' side go into their penultimate group game with a five-point lead over their nearest rivals and know a point will be enough to secure qualification for the first time since 2002.
Belgium have cruised through their campaign with seven wins and one draw at home to the Croatians in September last year, and Vertonghen says confidence is understandably high in the camp.
Vertonghen said: "We have reached the point where the national team has certain expectations. There are certain things we expect and demand of ourselves.
"We know Croatia will be one of the hardest games in the group, but nobody thinks it will go wrong. We are very confident, and we are strong enough to win in Zagreb."
Wilmots is likely to defy the wishes of Manchester United by playing Marouane Fellaini despite an ongoing wrist complaint, but Thomas Vermaelen is a doubt and Vincent Kompany and Christian Benteke are both missing .
Croatia are already assured of a play-off spot but can only pip the Belgians to automatic qualification if they win in Zagreb and in Scotland on Tuesday, while Belgium suffer an unlikely home reverse to Wales.
The Croatians have never quite recovered from their shocking 1-0 home defeat to Scotland in June and defender Vedran Corluka admitted it is up to the players to prove they deserve a place in the finals.
Corluka said: "There is no point looking back at what might have been. Although the Belgians are a class act they are not better than us. We showed that in Belgium and we will show that in Zagreb too."
In the other game in the group, Wales have the chance to claw their way off the bottom of the group if they beat fellow strugglers Macedonia in Cardiff.
The dismal Welsh campaign slumped to a new low with a 3-0 home defeat to Serbia last month while Macedonia will be looking for a rare double after beating Chris Coleman's men in Skopje.
Coleman has doubts over striker Sam Vokes and Arsenal midfielder Aaron Ramsey, but defender James Collins will go straight into the starting line-up after settling his dispute with the manager.