Highlights: Italy 1-1 New Zealand
New Zealand coach Ricki Herbert said his team can reach the last 16 but questioned some of the referee's decisions in the 1-1 draw with Italy.
Shane Smeltz gave the All Whites the lead but Italy levelled from the spot when Tommy Smith conceded a penalty after tussling with Daniele De Rossi.
Herbert said: "I thought some of the decisions were quite strange.
"The nation can come to the third game with us with a chance to go through - who'd have thought it?"
The result against the defending champions is the best in the history of a nation which still does not have a professional football league and is much more famed for its rugby exploits.
Smeltz feeling 'brilliant' after goal
Italy pressed for the three points in a pulsating second half, but New Zealand defended stoutly and could have snatched the win had Chris Wood not guided a late left-foot shot just wide.
"These boys just keep responding," added Herbert. "We knew we'd be up against it."
New Zealand captain Ryan Nelson described referee Carlos Batres's decision to award a penalty as a "ridiculous call".
Nelson speechless after draw with Italy
"I think their goal wasn't a goal. I think the guys will be disappointed that we ended up drawing because it was a dodgy goal," commented the Blackburn defender.
"It wasn't pretty, they [New Zealand] showed so much determination and guts."
Italy need to beat Slovakia on Thursday to guarantee their place in the second phase, but should they only manage a draw then New Zealand could deny them with victory over Paraguay in their final Group D match.
"I'm speechless because everybody put in such a shift. We've given ourselves an opportunity [to go through to the second stage]," continued Nelson.
"It's exciting. All we wanted to do was give ourselves an opportunity in the last game. Paraguay are just as good as Italy, an amazing team, so we're going to have to recover and do it all again."