The Black Caps will need to chase down a record score of 467 to claim victory over Australia in the first Test in Perth, the hosts declaring their second innings at 217/9 on day four.
Resumed at 167/6, and with a lead of 417 runs, Australia lost Pat Cummins early in the first session, spooning a simple chance to BJ Watling behind the stumps, out for 13.
Cummins' overnight partner Matthew Wade was the next batsman to fall, hitting a short ball from Colin de Grandhomme straight to Jeet Raval at deep square leg.
Mitchell Starc would be the last man to fall for Australia, caught at short third man to give Tim Southee his five-wicket haul, finishing with figures of 5/69.
Australia's last man Josh Hazlewood did not bat, captain Tim Paine declaring due to the paceman's injured hamstring, unable to bowl in the final innings.
The target will mean that the Black Caps have to bat out just over five sessions in order to try and win or save the match, heading into the Boxing Day Test in Melbourne next week.
One narrative for the Black Caps will be Ross Taylor's attempt to become New Zealand's all-time leading Test run scorer, needing 71 runs to surpass Stephen Fleming.
The highest run chase in a winning cause is 418 runs, achieved by the West Indies against Australia back in 2003.