But coach Buckingham — and the team — are keeping their feet on the ground.
"They are very focussed," said Buckingham. "As pleased as we are with the result, for us the performance is not a surprise. So you wouldn't have seen huge celebrations afterwards in terms of that side of things."
"It's one game and we have put ourselves in a good position to progress if we can pick up some points in the next two games. It's just a start but it's a very good start and a pleasing one to be involved in."
Honduras look likely to continue their record of never progressing past the group stages of this biannual event, despite qualifying eight times. They look the weakest of the four qualifiers this time from North and Central America.
New Zealand's next opponent, Norway, will be a step up. They eliminated defending champions England to qualify and also had a 1-1 draw with Italy .
The Scandinavians lost 3-1 to group favourites Uruguay on Saturday, and will need a result to stay in contention. A win will seal New Zealand's progression, while a draw will put them in a strong position.
The Junior All Whites have never beaten a European opponent at this level; they had tight one goal defeats to Portugal in 2011 and 2015, a 1-2 loss to Croatia in 2013 and a 0-0 draw with Ukraine in the opening game of the 2015 tournament.
The win over Honduras wasn't totally unexpected — they beat the same opposition 3-1 at the last Under-20 World Cup — but the commanding performance was a bonus.
Sarpreet Singh, Liberato Cacace, Callan Elliott, Gianni Stensness and Ben Wain (two goals) continued the form they had displayed for the Wellington Phoenix, while the youngsters developed at Wellington's Ole Academy (particularly Elijah Just and Callum McCowatt) were impressive.
"It was a real team effort," said Buckingham. "We have been fortunate to have two and a half weeks of good preparation and it helped to get to know the players a bit more. The biggest thing was getting them together for a period of time and involving them in the process of looking at our playing style and how we want to do things."
New Zealand went ahead in the eighth minute on Saturday, after a Honduran defender turned a Joe Bell cross into his own net.
Waine then scored twice in the space of 10 minutes, to seal the result with less than half an hour played.
His first came from a precise Just delivery, after Singh released the diminutive forward, and the second after some clever interplay between Cacace and Bell.
Just set up Singh for the fourth early in the second half, before substitute Matt Conroy scored an opportunistic fifth in injury time.
New Zealand play Norway on Tuesday (6:30am NZT).
