Hosts India declared their second innings at 284 for seven, having extended their overall lead to 283 runs at the Green Park.
Earlier in the day, debutant Shreyas Iyer (65) hit a patient half-century to rescue India from a precarious position. He had scored a hundred in the first innings.
Resuming at an overnight score of 14 for one, India lost four wickets for the addition of 70 runs in the morning session before Iyer, in the company of Ravichandran Ashwin and Wriddhiman Saha, strengthened the home team's position.
Iyer got out at the stroke of tea, but Saha carried on until the declaration came about.
For New Zealand, Tim Southee (3/75) and Kyle Jamieson (3/40) were the most successful bowlers.
Brief Scores: India: 345 and 234/7 declared in 81 overs (Shreyas Iyer 65, Wriddhiman Saha 22 not out; Kyle Jamieson 3/740, Tim Southee 3/75). New Zealand: 269 and 4/1 in 4 overs.