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Martin Guptil (21) was the only batsman to fall in the opening sesion as he was trapped leg before by fast bowler Umesh Yadav.
Tom Latham (25 batting) and Kane Williamson (21 batting) were at the crease when lunch was called.
New Zealand now trail the hosts by 247 runs with nine wickets remaining.
With the pitch beginning to show signs of wear and tear, the Indian bowlers got a fair amount of turn and movement off the wicket.
But despite the challenging conditions, the New Zealand batsmen stil managed to maintain a decent scoring rate.
The visitors suffered their first blow in the 10th over with Guptill, who seemed to be in good form, beaten by an inswinger from Yadav.
The ball moved very slightly after pitching around the off-stump before hitting Guptill's pads in plumb in front of the middle stump.
Guptill smashed three boundaries during his 31-ball knock.
Williamson then joined Latham in the middle and the duo ensured that the visitors lost no more wickets before lunch.
Earlier, the hosts were bowled out for 318 runs in the opening session of Day Two at the Green Park Stadium here.
The Men in Blue scored 27 runs in seven overs to get past the 300-run mark in their historic 500th Test.
Resuming the day on 291/9, Ravindra Jadeja scored an unbeaten 42 from 44 balls with seven boundaries and a six, putting on an invaluable stand of 41 runs for the final wicket with Yadav, who survived 15 balls before gloving a short ball from pacer Wagner to New Zealand wicketkeeper Bradley-John Watling for nine runs.
For New Zealand, spinner Mitchell Santner and fast bowler Trent Boult claimed three wickets each, while Wagner bagged a couple. Inderbir Singh Sodhi and Mark Craig got one wicket each.
New Zealand (first innings) 71/1 (Tom Latham 25 batting, Kane Williamson 21 batting) vs India 318 (Myrali Vijay 65, Cheteshwar Pujara 62, Ravindra Jadeja 42 not out; Trent Boult 3/67, Mitchell Santner 3/94)
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