The world's No. 1 ranked team, who beat England 26-5 in the semifinals earlier in the day, have been impressive throughout the tournament and after tries from Portia Woodman and Michela Byde the Kiwis led at half-time 12-0.
But roared on by the home crowd, the Aussies fought back in the second half.
A try from co-captain Emilee Cherry got them back into the contest and with a minute remaining on the clock, Ellia Green used her blistering pace to level the scores.
Australia could have gone ahead in the final few seconds of the match but they missed their conversion kick.
Deep into overtime, Australia then won possession and looked to have an opportunity for one last attack, but instead Cassie Staples kicked the ball into touch taking the game into extra-time.
It was a decision that would prove costly.
Knowing that the first score would end the game, extra-time started in a scrappy fashion. With the searing heat bearing down on the players and tiredness showing on both sides, there were fumbles and plenty of other errors.
It looked as if the game would need one more period of extra-time to decide the contest, but then Kelly Brazier of New Zealand took possession close to her own goal line.
The 28-year-old shimmied past one player, dropped her shoulder to move past the next, and accelerated away, leaving three Australian defenders in her slipstream.
"I'm probably not the quickest, but I pride myself on my fitness. Obviously it was 19 minutes in so I had a bit of a look around and thought it's now or nothing, so just went for it," Brazier told New Zealand website Stuff.co.nz
after the game.
"I had a few chasing but just thought I'm gonna go and it paid off in the end."
Running nearly the entire length of the field she made the historic try, collapsing in exhaustion at the goal line as her teammates piled on top of her to celebrate.
"All I could feel was my lungs going up and down in the air. I was just worried about trying to catch my breath back and then the girls just jumped on top of me so it made it a bit hard to breathe. So I was just trying to breathe, that was it," Brazier added.
Both teams were in tears at the end, some from ecstasy, some from despair. It was a thrilling end to an exciting tournament that is likely to only help continue to promote and grow women's rugby sevens.