Brendon McCullum and Daniel Vettori's 126-run partnership means the first Test with Australia will go into a final day.
New Zealand began the day on 187-5 in their second innings after being forced to follow on and seemingly heading for an innings defeat to Ricky Ponting's men.
But, on a day that was reduced to just 52 overs because of rain, the Black Caps reached 369-6, with Vettori eventually falling for an excellent 77 and McCullum unbeaten on 94.
The duo's 126-run stand means that, with a lead of 67 and four wickets still intact, the match will go into a fifth day, with the home fans hoping for a rearguard action to frustrate the Aussies on the final day.
McCullum has hit 11 fours and a six in his innings to date and he will be the main threat to Australia's chances of victory on day five at the Basin Reserve but, with good weather forecast for Tuesday, the visitors will be strong favourites to wrap up the match at some stage.
Vettori's 77 came from just 119 deliveries and confirmed his status as a genuine all-rounder.
Off-spinner Nathan Hauritz took the wicket of the Black Caps' skipper and he has so far toiled away for 3-119 from 49 overs.
Daryl Tuffey hit two fours and a six in his unbeaten 23 and he will resume with McCullum on the final morning as the Kiwis look to somehow wriggle out of the match with a draw.