In-form first drop Usman Khawaja was out edging for 24 in Sunday's fourth over as the tourists slipped to 2-67.
Needing to avoid defeat at Hagley Oval to top the International Cricket Council's rankings, Australia looked in strife.
But Burns and Smith battled through the opening onslaught from Trent Boult, Tim Southee and Matt Henry.
Burns has produced the finest moment of his 10-Test career with his knock. The 26-year-old was watchful throughout, likewise skipper Smith.
Both batsmen were unconvincing early but the runs came freely after a testing opening hour. The second new ball will be available soon after tea and the Black Caps sorely need it.
Henry had Burns caught behind on 35 but the opener successfully used the Decision Review System (DRS) to overturn his dismissal.
The Queenslander was in two minds about whether to play the short delivery. Burns was more certain about reviewing umpire Ranmore Martinesz's verdict, with replays confirming the ball came off his bicep. Otherwise neither batsman has offered a genuine chance.
Wagner sent down a bouncer barrage to Smith in the morning then struck him in the shadows of tea. Boult inflicted a painful blow to Smith's midriff in the penultimate over of the first session. None of it rattled the 26-year-old, who dug in alongside Burns.
It may not have been as entertaining as Brendon McCullum's world-record knock on day one but it was damn effective. The pitch, so green and wet on day one, has flattened out.
Part-time offspinner Kane Williamson delivered two overs at the end of the morning session as McCullum tried to conjure a wicket.
Pundits are already questioning the merits of NZ's decision to omit tweaker Mark Craig and bank on a four-prong pace attack.
-AAP