In the second innings on Day 4, Australia were reduced to 80/5, after Travis Head's departure, with 199 still needed for the series win. The duo of Mitchell Marsh and Alex Carey stepped up to put together a match-winning stand of 140 runs in 29 overs.
Marnus Labuschagne's gritty 56 off 52 saw Australia reach a modest total by the end of allotted 50 overs.
In the wake of the novel coronavirus, Cricket Australia has announced that the ongoing series will be played in front of empty stands.
The only difference between squads for Australia's series against South Africa and New Zealand is Jhye Richardson, who will not feature against Blackcaps.
Nathan Lyon took the wickets of Tom Blundell (49), Jeet Raval (31), William Somerville (0), Neil Wagner (0) and Matt Henry (3) to return with 5/68.
Having won the first Test as well, Australia have now taken an unassailable lead of 2-0 in the three-match series with the last Test to be played in Sydney.
New Zealand tailender Mitchell Santner survived a controversial caught-behind review, while the replay showed the ball took a slight touch of his gloves.
New Zealand began the day already in trouble on 44 for two, having lost batting kingpin Kane Williamson and makeshift opener Tom Blundell.
Tim Paine expressed his discontentment after getting out by a controversial DRS decision and then seeing Ross Taylor getting saved by the TV Umpire.
Wagner returned figures of 4 for 83, while Tim Southee ended with 3 for 103.
