Replying to Australia's imposing total of 459 for five declared, New Zealand were precariously placed at 108 for the loss of four wickets on the second day of the Basin Reserve Test.
Holding fort for New Zealand were skipper Daniel Vettori on 42 and Martin Guptill on an unbeaten 19.
Thanks to Vettori and Guptill, New Zealand recovered from a wobbly 43 for four to 108 without further loss of wickets. The home side is still 152 runs away from avoiding follow-on.
Vettori picked the right balls to hit in his 79-ball knock, including five fours, while Guptill, now ensconced at No 5, played a mature hand with his side in trouble. He batted 113 minutes and 94 deliveries, with his only extravagant shot a big straight six off spinner Nathan Hauritz.
Left-arm paceman Doug Bollinger, with figures of two for 21, relished a bouncy pitch as he bookended the New Zealand top-order collapse.
He started the rot in the first over when he trapped BJ Watling dead in front with a fast inswinger, first ball.
New Zealand didn't need any more run out dramas but Tim McIntosh provided them when he pushed into the off side and called Peter Ingram through.
It was risky, and bowler Mitchell Johnson obliged brilliantly when his right foot kick hit the stumps with the unlucky Ingram, on five, short.
McIntosh's unhappy 74-minute stay for nine ended when he edged debutant Ryan Harris to the slips cordon for the Queenslander's first Test wicket.
Big hope Ross Taylor looked comfortable immediately, stroking four boundaries en route to 21, but a fired-up Bollinger returned and enticed an edge, leaving Vettori to marshall another rescue mission.
It was all Australia for the first half of the day, too, as Michael Clarke's 168 and Marcus North's 112 not out featuring in a record-breaking partnership that batted the hosts out of the test.
From 316 for four overnight, the pair rumbled on in perfect conditions as they put on 253, an Australian fifth wicket partnership record against New Zealand, beating the previous mark of 213 set by Greg Matthews and Greg Ritchie in the 1985-86 season.
Clarke's was the only Australian wicket to fall on Saturday when he charged Vettori and was stumped down the leg side by Brendon McCullum.
His epic innings, a 14th Test century for the Australian vice-captain, spanned 364 minutes, 253 deliveries and included 22 fours and two sixes.
A jubilant North reached his fourth century in his 14th Test soon after Clarke's departure as he top-edged Chris Martin over McCullum's head for four.
North had batted exactly five hours when captain Ricky Ponting boldly called time on the innings, 50 minutes after lunch.
Debutant Brent Arnel was the most successful New Zealand bowler with two for 89 off 26 overs. Vettori toiled for 33 overs to take one for 111 off 33, while Martin was the only other wicket taker with one for 115 off 30.