India were all out for 325 during the second session with Ajaz Patel entering the history books.
Indian bowlers then ran through New Zealand batting with Mohammed Siraj taking three wickets.
Resuming the day at 221 for four, India scored 64 runs in the morning session with the loss of two wickets. They added another 40 runs for four wickets after lunch.
India lost Wriddhiman Saha (27) and Ravichandran Ashwin off successive balls early in the morning session before Mayank Agarwal (150) and Axar Patel (52) took the score past 300-run mark.