The Juventus forward hauled Italy level following a debatable decision after former Halifax striker Shane Smeltz had handed New Zealand a shock early lead at the Mbombela Stadium.
Italy dominated a compelling Group F contest thereafter but could not find a way past outstanding goalkeeper Mark Paston. The surprise result keeps alive New Zealand's hopes of reaching the second round for the first time in their history and leaves Italy with much still to do.
The All Whites, buoyant after their last-gasp equaliser against Slovakia, made the perfect start as Smeltz crept into the box to give them a seventh-minute lead.
Italy coach Marcello Lippi had warned New Zealand's greatest threat would come from set-pieces and his side were caught out as Simon Elliott swung in a free-kick from the left. The ball dipped over Alberto Gilardino and Leo Bertos and wrong-footed Fabio Cannavaro, who could only divert it into the path of Smeltz. The Gold Coast forward, who has also played for Mansfield and AFC Wimbledon, gleefully accepted and poked past second-choice goalkeeper Federico Marchetti.
Italy responded with a free-kick from Claudio Marchisio bouncing awkwardly and forcing Paston to save.
New Zealand were incensed when Rory Fallon was booked for catching Cannavaro in the face and replays did suggest contact had been minimal. Italy complained soon after when Fallon's elbow appeared to connect with Giorgio Chiellini but this time Guatemalan referee Carlos Batres was lenient.
Moments earlier Chiellini had stabbed wide when well placed and then Riccardo Montolivo hit the post with a long-range shot as Italy stepped up the pressure.
New Zealand were caught out after 28 minutes as Daniele de Rossi went down in the area after the slightest of shirt pulls from Ipswich defender Tommy Smith. The Kiwis complained about the decision but Iaquinta stepped up to convert from the spot, much to Italian relief.
New Zealand recovered their composure but Paston made a good save from a 20-yard De Rossi effort in first-half injury time. Italy played at a slower tempo in the second period but dominated possession.
Half-time substitute Antonio di Natale threatened with a smart shot on the turn but Paston was equal to the half-volley. Iaquinta controlled on the edge of the area but Winston Reid did enough to force him to fire wide as he turned.
New Zealand struggled to break out of their own half and it was not until just after the hour they threatened again, Ivan Vicelich firing narrowly wide after a Cannavaro clearance fell invitingly.
The introduction of Mauro Camoranesi gave Italy extra drive and he put Montolivo through to force a fine save from Paston from 25 yards. Reid then claimed to have been caught in the face by Chiellini and stayed down as Italy attacked but the Danish-born defender soon recovered.
Italy's urgency increased as time ran down but Camoranesi and Di Natale both shot wide and Chiellini missed the target with a header.
Kiwi substitute Chris Wood, of West Brom, almost caught Italy off guard on a rare counter-attack eight minutes from time but shot across goal.
In a frantic finish Camoranesi then tested Paston from long range and Ryan Nelsen blocked well from Iaquinta as New Zealand held on for a famous draw.