The visitors trail India by two runs.
Devon Conway and Will Young were batting on 15 and 8 respectively when tea was taken.
Earlier, left-arm-spinner Ajaz Patel (5/103) took five wickets to help dismiss India for 263 in their first innings.
Shubman Gill, who was unlucky to miss out on a century, anchored India's innings with a 146-ball 90 while Washington Sundar, who scored a brisk 38 off 36 deliveries, helped India take a slender 28-run first innings lead.
Rishabh Pant (60) scored an entertaining fifty in the morning session.
Brief Scores: New Zealand 235 all out and 26 for 1 in 9 overs (Devon Conway 15 batting ; Akash Deep 1/9) India: 263 all out in 59.4 overs (Shubman Gill 90, Rishabh Pant 60; Ajaz Patel 5/103).