Mitchell Santner takes four wickets
Resuming at 16-1, India now trails New Zealand by 152 runs after the visitors set a target of 259. Santner's left-arm spin proved devastating as he took four wickets, including the crucial scalp of Virat Kohli for just one run. Off-spinner Glenn Phillips supported with two wickets.
At the break, Ravindra Jadeja (11) and Washington Sundar (2) were at the crease, with India at risk of falling further behind.
Overnight batsmen Yashasvi Jaiswal and Shubman Gill started cautiously before Santner struck in the 11th over, trapping Gill lbw for 30. The home crowd fell silent when Santner bowled Kohli with a low full toss.
Phillips quickly followed up, dismissing Jaiswal, caught at slip for 30, and bowling Rishabh Pant for 18 to leave India reeling at 83-5. Santner later had Sarfaraz Khan caught at mid-on for 11 and trapped Ravichandran Ashwin lbw for four.
Earlier, Sundar made a strong return to the Test side with 7-59, helping bowl out New Zealand, who saw solid contributions from Devon Conway (76) and Rachin Ravindra (65). New Zealand, led by Tom Latham, is aiming for their first series victory in India since 1988 after winning the opening match.