Missed tackles and fumbled ball didn't help New Zealand's cause in the first half and when Tomasi Cama was sin-binned for a dangerous tackle after four minutes, Australia was quick to pounce, with a try by Ed Jenkins.
That was followed by another try under the posts by Jacob Taylor, with the conversion made by Bernard Foley, putting Australia ahead 12-0 at the break.
Greg Jeloudev scored the opening try of the second half, putting Australia further ahead.
But New Zealand pulled themselves together and Scott Curry scored under the posts, with Buxton Popoalii converting to finally put some points on the board.
Another try quickly followed from Tim Mikkelson, but it was too late to have any bearing on the eventual outcome.
Earlier New Zealand beat England 26-12 in the quarterfinals at Murrayfield, having dispatched Russia 43-0, France 43-5 and Argentina 38-7 in pool play.
Coach Gordon Tietjens' men have already secured New Zealand's ninth title from 12 attempts in the world series. They have 150 points, 29 more than second-placed England, while South Africa were a further five points adrift in third heading into the last round in the Scottish capital.
Result: Australia 19 (Ed Jenkins 1, Jacob Taylor 1, Greg Jeloudev 1, Bernard Foley 2 con)
New Zealand 12 (Scott Curry 1, Tim Mikkelson 1, Buxton Popoalii 1 con). Halftime: 12-0.
