Joe Burns and Usman Khawaja had Australia in sight of victory after an absorbing fourth day of the second Test on Tuesday marked by stubborn resistance from New Zealand.
With Burns on 27 and Khawaja 19, Australia were 70 for 1 at stumps requiring a further 131 at Hagley Oval here to sweep the series and reclaim the world number one ranking.
Jackson Bird, with his first five-wicket Test haul, and James Pattinson combined to end the New Zealand second innings at 335, giving Australia a 201-run target.
Burns offered chances but luck was on his side. On 19, he pulled Henry through square leg where Wagner was unable to hold a difficult chance.
Although Australia have been dominant for much of the Test, New Zealand put up a valiant fight with two century partnerships as they battled to save the contest.