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.
New Zealand team management had to ask batting coach Peter Fulton, a veteran of 23 Tests, to be ready in case he was required to field.
Notably, New Zealand have already lost the series after losing the first two matches by 296 and 247 runs to Australia.
Marnus Labuschagne made 215 off 363 deliveries before his marathon knock was ended caught and bowled by spinner Todd Astle.
Matthew Wade was batting on 22, along with Labuschagne at the end of the day.
Australia won the first test by 296 runs in Perth and the second at the Melbourne Cricket Ground by 247, both in four days.
