India will be looking to push towards a morale-boosting win after spinners Ravindra Jadeja and Ravichandran Ashwin helped them take the upper hand on Day 2.
On a pitch offering a lot of assistance to the spinners, Jadeja took 4/52, while Ashwin returned to form with figures of 3/63 to reduce New Zealand to 171/9 in 43.3 overs.
The visitors lead by 143 runs with just one wicket in hand.
Will Young was the lone Kiwi batter to offer some resistance as he made 51, while no other batter got above the 30-run mark.
New Zealand were 93/3 at one stage before Jadeja and Ashwin did the damage as the Kiwis lost six wickets for 78 runs.
India will be looking to claim the last wicket quickly and finish off New Zealand's second innings and then chase down the runs to avoid a series whitewash at home.