Ahinkya Rahane (25 batting) and Hanuma Vihari (15 batting) were the two unbeaten at the close of play as India faced 65 overs in their second innings.
Opener Mayank Agarwal made a fine 58.
Prithvi Shaw (14), Cheteshwar Pujara (11) and skipper Virat Kohli (19) all got out after starts.
Trent Boult (3/27) was pick of the bowlers for New Zealand in India's second innings.
New Zealand were earlier bowled out for 348 in their first innings in reply to India's below-par 165.
Resuming at the overnight score of 216 for 5, New Zealand added 132 runs in the morning session.
Skipper Kane Williamson top-scored for New Zealand with 89.
Ishant Sharma was the star performer with the ball for India with figures of five for 68, while off-spinner Ravichandran Ashwin scalped three wickets giving away 99 runs.
India: 165 all out & 144 for 4 (Mayank Agarwal 58, Ajinkya Rahane 15 not out, Hanuma Vihari 15 not out; Trent Boult 3/27).
New Zealand: 348 all out in 100.2 overs (Kane Williamson 89, Ross Taylor 44, Kyle Jamieson 44; Ishant Sharma 5/68, Ravichandran Ashwin 3/99).