Mitchell Marsh and Alex Carey half-centuries raised Australian hopes at lunch Monday on a tantalising day four of the second Test against New Zealand in Christchurch.
Australia were 174-5 at the break at Hagley Oval, requiring a further 105 runs for victory while New Zealand need five more wickets.
Marsh was not out on 55 with Carey on an unbeaten 50 in a sixth-wicket partnership worth 94.
The momentum was with New Zealand at the start of the day, with Australia resuming at 77-4, and then the tourists lost Travis Head in the second over.
After rain delayed the start of play by an hour, Tim Southee pitched a ball outside off-stump to Head that was slashed to Will Young at point and he was gone for 18.
Marsh survived a similar fate on the previous delivery, again outside off-stump, when he was dropped by Rachin Ravindra at backward point and scampered through for a single.
The New Zealand pace trio of Southee, Matt Henry and Ben Sears were getting swing in both directions.
But the hosts did not help themselves with leg byes and byes gifting Australia an extra 20 runs, 12 of them off the fourth seamer Scott Kuggeleijn.
Carey, who replaced Head, used attack as his best means of survival with his 50 coming off 61 deliveries.
He had one heart-stopping moment on 19 when given out lbw to a Henry ball that swung in sharply. Australia sought a review and the ball tracker showed the delivery would have missed the stumps.
New Zealand have only beaten Australia eight times in 62 Tests with their last success 13 years ago in Hobart.
It is 31 years since the Black Caps last beat Australia in a Test match on New Zealand soil.
Australia won the first Test of the two-match series. (BSS/AFP)