Tom Latham was 33 not out and Kane Williamson was unbeaten on 10 after Martin Guptill was dismissed for a duck in the fourth over — the seventh wicket to fall in the second session.
Earlier, South African-born Neil Wagner returned career-best bowling figures of 6-106 as New Zealand dismissed Australia for 505 in reply to its first innings of 370, a lead of 135.
Australia's lead seemed likely to be much greater until Wagner crashed through its middle and lower order to claim his second haul of five wickets or more in tests. His previous best in 19 matches was 5-64 against Bangladesh in 2013.
Wagner unleashed a barrage of short-pitched bowling with an old ball on a docile pitch to curb Australia's scoring after it had started the third day only seven runs behind New Zealand.
The critical wicket Monday was that of Adam Voges (60) who is in the richest form of his career, having scored 269 not out, 106 not out and 239 in his last three innings — the latter in the first test at Wellington.
As long as Voges was at the wicket, averaging 97 in 15 tests, there was a strong likelihood Australia would amass a substantial first innings total and lead.
The day at first seemed to be heading in that direction as Voges put on 85 for the fifth wicket with nightwatchman Nathan Lyon who batted 106 minutes for 33. Lyon went to the wicket late Sunday on the dismissal of Steve Smith for 138.
Smith had put on a record 289 runs for the third wicket with Joe Burns, who made 170.
Australia needs only a draw to win the two-match series after winning the first test by an innings and 52 runs and to take over from India as the top-ranked test nation.
Wagner dismissed both Smith and Burns late Sunday and then removed Voges early in Monday's second session, triggering Australia's slide.
Voges had batted 157 minutes when he was drawn into a hook by Wagner and picked out Latham, and Australia lost its last five wickets for 41 runs in pristine batting conditions.
Mitch Marsh (18) mis-timed a pull shot and provided a catch to Henry Nicholls at short mid-wicket.
Corey Anderson interupted the flow of wickets for Wagner, dismissing James Pattinson (1), then wicketkeeper Peter Nevill (13) tried to ramp a bouncer over the slips cordon, top-edged and was caught by his Kiwi opposite B.J. Watling.
Wagner then had Josh Hazlewood (13) caught by Brendon McCullum, giving the New Zealand captain his second catch of the innings.
McCullum took a brilliant catch at slip to dismiss Lyon from the bowling of Kane Williamson. After scoring the fastest century in test history, from 54 balls, during the New Zealand innings, McCullum showed he's also no slouch with the ball, bowling four overs at a cost of three runs.
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