"We just needed to relax the guys ... we needed a couple of runners on base to create some pressure and an opportunity.
"We weren't able to capitalise on it an inning before, but in the sixth inning, we were able to load the bases and then Joel Evans comes up with probably the biggest hit of his career."
With just one inning left to respond, Australian slugger Nick Shailes also "went yard" to narrow the deficit 6-4, but it was a case of too little, too late.
Black Sox relief pitcher Nick Hayes held his nerve to secure the last three outs, striking out Brendan O'Byrne and James Todhunter, before Andrew Kirkpatrick grounded out.
New Zealand had opened the scoring in their first at-bat, when captain Nathan Nukunuku's sacrifice fly-ball brought lead-off batter Campbell Enoka home.
But as Black Sox pitcher Josh Pettett began to struggle with his control, the Aussies answered with two runs in the third inning and another in the fourth to take the lead.
The Kiwis got one back in the fifth inning, when they filled the bases and veteran Brad Rona's sacrifice brought Enoka home.
They weren't able to take full toll of that opportunity, though, and needed Evans' heroics in their next turn at bat to seal the comeback.
New Zealand had made 10 consecutive world championship finals, with their last victory coming under very similar circumstances against Venezuela at North Harbour's Rosedale Park four years ago.
On that occasion, captain Rhys Casley hit a three-run homer in the third innings for a 4-1 victory.
But this was their first success on Canadian soil, where the home team were defending champions entering this tournament.
The Black Sox made the final by defeating Canada 12-11 in a thriller yesterday, before Australia reduced the hosts to the bronze medal in a playoff earlier today.
