The 369-run target represented a record chase for the hosts and their slim hopes were all but extinguished in the seventh over of the morning.
Having resumed on 56 not out, Rachin Ravindra got himself out cutting Nathan Lyon, and three balls later an inside edge saw Tom Blundell depart for a duck.
Lyon’s next over essentially sealed the result, trapping first-innings top-scorer Glenn Phillips deep in his crease for 1.
That completed the offspinner’s 24th five-wicket bag and confirmed the Black Caps had for the second test in a row erred in opting for four seamers over a frontline spinner.
A couple of those seamers added some quick runs, Scott Kuggeleijn scoring 26 and Matt Henry 14, while at the opposite end Daryl Mitchell (38) played a lone fighting hand.
Lyon soon completed a 10-wicket haul for the test as the tourists sealed the match in a dominant first session.
Player of the match Cameron Green’s unbeaten 174 was the decisive innings in the test, helping Australia to the only total that exceeded 200 on a challenging pitch.
New Zealand are still without a home test victory over Australia since 1993, having beaten their transtasman neighbours only once in their last 32 meetings.
The Black Caps will have a few days to find answers before the second and final test starts at Hagley Oval in Christchurch on Friday.