The captain of the All Whites, Ryan Nelsen, says he hopes everyone appreciates and celebrates the history that was made at the Football World Cup in South Africa on Wednesday.
New Zealand gained its first ever competition point after scoring a 1-all draw with Slovakia in Rustenberg.
The Slovakians dominated the game and scored early in the second half, but the All Whites defender Winston Reid headed home the equaliser three minutes into stoppage time.
All Whites striker Rory Fallon says the team can "kick on and do even better".
"That's the beautiful thing about our team - that we believe that we can do it, " a jubilant Fallon said.
It is 28 years to the day that Fallon's father Kevin helped coach the All Whites in their opening 1982 match, a 5-2 loss to Scotland. The 1982 side lost all three games.
Sam Malcolmson, who also played in the 1982 side, says the result shows that New Zealand could be a real threat to Italy in its next game, and is a contender to reach the second round of the tournament.
All Whites coach Ricki Herbert has hailed the result as one of the best in New Zealand footballing history.
And captain Ryan Nelsen says he hopes the result will dispel the belief that the team don't deserve to be there. He says he told them before the game that "it will take a few seconds and you can etch your name in history".
New Zealand next play the defending champion Italy early on Monday morning.
Equaliser scored in stoppage time
In a game dominated by the Slovakians, the score was still 0-0 at half-time, but a well-timed header by Slovakia's Robert Vittek found the goal five minutes into the second half.
Despite some strong pressure from Slovakia after the break, the New Zealand defence kept their goal intact.
In the final minute of stoppage time, Denmark-based defender Winston Reid scored the pivotal equaliser by heading in a Shane Smeltz cross.
Reid, who almost agreed to play for Denmark before the tournament, got yellow-carded for removing his jersey in wild celebration.
Slovakia 'paid for sitting on lead'
The BBC's reporter at the game says Slovakia paid for sitting back on their lead. While looking comfortable in defence, the Slovakians did not seem desperate to press home their superiority.
Their attitude was summed up when Vittek, given a chance to put his side two goals ahead and wrap it up, appeared to delay too long, allowing Reid to slide in with an excellent tackle.
And it was Reid, the BBC says, who was the New Zealand hero at the other end, capitalising on a "perfect ball" from Smeltz.
The ABC says that the All Whites were weak on attack but that their defence, marshalled stoutly by Nelsen, showed great desperation and purpose to scramble across and keep thwarting the Slovakians.
The Italian sports paper La Gazzetta dello Sport says that despite New Zealand's late heroics, Italy can "sleep soundly" considering the showing of their two other Group F opponents.
