Both still have the chance of advancing to Round of 16.
Both Marcello Lippi and Ricki Herbert did not make any changes to their outfield starting XI from the first matches in Group F, although the champions did switch from a 4-2-3-1 formation to a more comfortable 4-4-2 and Federico Marchetti replaced the injured Gianluigi Buffon as goalkeeper.
New Zealand remarkably took the lead on seven minutes. A set piece was floated in by Simon Elliott and Smeltz pounced from close range after Fabio Cannavaro failed to clear the ball.
There was potentially an offside, as Winston Reid had flicked on the free-kick, but the goal stood after the ball came off the Italian captain.
It was Gianluca Zambrotta who then tested his luck from long range and wasn't far away from finding the top corner with 20 minutes gone. The Azzurri were growing in confidence and Riccardo Montolivo's low drive from 25 yards hit the post.
Tommy Smith tried to defend Daniele De Rossi in the area, getting a hold of his jersey, and the Roma star went to ground easily to earn a spot-kick, which Iaquinta converted leaving goalkeeper Mark Paston with no chance.
Towards the end of the half, the Azzurri had plenty of possession and were patient when trying to carve out chances, but New Zealand continues to sit deep and hold them at bay as the initial 45 minutes ended 1-1, although Paston had to get a hand to De Rossi's powerful effort.
Lippi made two changes to start the second-half in order to add some bit to their attack, Antonio Di Natale and Mauro Camoranesi entered for Gilardino and Simone Pepe.
It was Serie A's top-scorer this past season that made an immediate impact, as his volley from a tight angle was saved by the goalkeeper.
Herbert's men were pinned back futher and further, but held their shape well as they looked to keep out the Europeans, who struggled to find a breakthrough by the hour mark.
On a rare opportunity for New Zealand, midfielder Ivan Vicelich hit a vicious strike from just outside the area, but it whizzed just wide of the post.
Montolivo responded with a dipping effort, but Paston made a fantastic stop to keep out the Italians with 20 minutes left.
La Nazionale went on a swift counter, but Nelsen cleared the ball from inside the six yard box as his side went closer to a precious point against the 2006 World Cup winners.
Waves of attack came from the four-time champions, but Di Natale's shot did not trouble the 'keeper once he escaped the intentions of the opponent's defence.
Italian supporters had their head in hands as Wood's shot flashed across the face of goal and missed by inches as space began to open up for them on the counter.
Camoranesi hit a brilliant shot from 30 yards, but Paston once again provided the crucial save with just minutes remaining.
The final whistle blew with Italy and New Zelaand both on two points and a win for either side would guarantee them passage into knock-out stages on the final match-day of the group stage.