Brendon McCullum's unbeaten 94 and skipper Daniel Vettori's 77 helped pull New Zealand off the mat and take a 67 runs lead against Australia at end of fourth day play in Wellington's Basin Reserve.
New Zealand were 369 for six in their second innings at stumps on a rain-shortened fourth day.
McCullum is six runs short of his fifth Test century after a heroic rescue act left New Zealand to fight another day in the first Test against Australia.
New Zealand with just a 67 runs lead needs to bat nearly two sessions on Tuesday to head to the second Test in Hamilton with an unlikely draw.
"There was some good fight shown, it was great to see. We're giving ourselves a good chance of saving the Test and maybe even get into a position where we can put them under pressure to possibly even win the Test," said opener Tim McIntosh.
Playing his 50th Test, McCullum frustrated the Australian attack for 215 minutes and 178 deliveries before bad light and showers forced an early end, Stuff.co.nz reports.
It could be McCullum's best Test innings yet if New Zealand saves the match after they followed on 302 behind.
McCullum and Vettori posted a record sixth-wicket stand against Australia of 126, before Tuffey helped add an unbroken 60 in 71 minutes.
Vettori took charge early, breezing to 50 off 64 balls as he cut, drove, hooked and shuffled.
His only life was on 60 when he chipped a ball through Johnson's fingers on his follow through, and he and McCullum soon passed Stephen Fleming and Chris Cairns' sixth wicket record of 110 on the same ground 10 years ago.
Hauritz finally removed Vettori when he played a sweep on to leg stump after a vital three-hour vigil.