Chasing an unlikely 488 for victory at the MCG, the Black Caps lost Tom Latham caught behind before Kane Williamson and Ross Taylor followed.
Williamson's duck was dramatic. He was given out lbw on field by Marais Erasmus before ball-tracking confirmed the umpire's call as it was only clipping leg stump.
It followed Australian captain Tim Paine expressing doubt over the technology after a number of controversial calls on day two of the Test.
The dismissal also capped a horrible Test for Williamson, who won the toss and opted to bowl only for Australia to amass 467 first innings runs. He then scored just nine himself in his opening knock.
Taylor followed him four balls later, chopping on while going at one from outside off stump.
Latham's wicket was more straight forward, caught behind trying to drive Pattinson to a full ball well outside off stump.
The Aussies earlier declared at 5-168 midway through Sunday's morning session, with Matthew Wade not out on 30.
After being flogged by 296 runs in Perth, New Zealand must at least draw the match in Melbourne to have a chance of maintaining their three-year unbeaten run in Test series.
The Black Caps have not lost a series of the seven they've played since early 2017.
However surviving at the MCG appears an insurmountable task.
No team has successfully chased down more than 418 in 142 years of Test cricket and New Zealand have not faced more than 66 overs in an innings this series.
They have scored a measly 485 runs across their three knocks.
