The Kiwis were in deep trouble when bad weather intervened and forced play to be abandoned before the final session of the fourth day, leaving them needing to survive the final day to force a draw.
Australia captain Ricky Ponting had already enforced the follow-on after New Zealand were dismissed for 244 at tea -- 326 runs short of Australia's massive total of 570 for eight declared.
However, play was called off before the Kiwis had begun their second innings when the heavens opened and the covers were placed on the pitch.
"Hopefully it's still raining tomorrow," New Zealand batsman Lou Vincent told reporters.
"We're going to go out tonight and do some rain dancing."
Monday's first session had also been washed out but the Australians still managed to bowl New Zealand out when the sky briefly cleared between lunch and tea.
New Zealand had resumed at 122-4 in their first innings but lost their last six wickets for 78 runs to give Ponting the chance to push for victory.
"It's a bit of guesswork the weather round here," Australian fast bowler Michael Kasprowicz said.
"I think we back ourselves to make some early impact and then keep doing our things.
"But we certainly don't take anything for granted with the New Zealand side and the wicket's playing exceptionally well and very flat."
Vincent top-scored with a patient 63 off 164 balls after starting the day on 38, while Daniel Vettori smashed eight boundaries in making a brisk 45 off 63 deliveries.
Kasprowicz and leg spinner Shane Warne captured three wickets each for Australia while Glenn McGrath got two and Jason Gillespie and Michael Clarke one apiece.
Vincent and night watchman James Franklin made a bright start, adding 58 for the sixth wicket before Franklin got a thick edge to Kasprowicz on 26 and wicketkeeper Adam Gilchrist took a simple catch.
Vincent had reached his half century off 115 balls but his resistance finally gave out when he also nicked Kasprowicz to Gilchrist, giving the Queensland bowler his 99th test wicket.
Warne, the world record holder for test wickets, mopped up three of the last four wickets while Gillespie bowled Iain O'Brien with a yorker.
Warne got rid of wicketkeeper Brendon McCullum when he spooned a catch to Michael Clarke at cover then bowled Craig McMillan for 20.
Vettori frustrated the Australians for over an hour with a lusty display before he was caught on the boundary off Warne.