The only success thus far for the hosts was the wicket of Martin Guptill, trapped in front by Umesh Yadav for 21.
Earlier, overnight batsman Ravindra Jadeja contributed a useful 42-run cameo for the hosts, who had started the day on 291 for nine.
Murali Vijay's 65 was the top score of the innings for India.
New Zealand bowlers Trent Boult and Mitchell Santner claimed three wickets each.