As Indian opener Shikhar Dhawan fell cheaply for five, Rohit Sharma and Vijay Shankar injected some momentum before the latter was dismissed for 43.
To support the Hitman, Rishabh Pant came out to share the crease. However, the wicketkeeper could not build a solid much-needed partnership and returned for 28, which opened the flurry of Indian wickets. Dhawan fell for 38 in the very next over.
Hardik Pandya and former captain MS Dhoni, too, could not stay longer at the crease. Dhoni fell cheaply for two while Pandya returned with a double-digit score of 21.
Having required 16 runs off last over, Dinesh Karthik and Krunal Pandya displayed their cameo but could not seal the series-decider match for India. Karthik and Pandya remained unbeaten on 33 and 26, respectively.
Earlier, New Zealand exploited the batting-friendly conditions and posted an imposing 212 runs for the loss of four.
Opener Colin Munro, who was adjudged Man of the Match, smashed a 40-ball 62 and shared an 80-run partnership with Tim Seifirt to lay the foundation for a big total after the Indian captain opted to bowl.
The Kiwi players kept ticking the scoreboard as New Zealand skipper Kane Williamson contributed 27, while Colin de Grandhomme blazed a crucial 30-run cameo.
For India, left-arm spinner Krunal Pandya was the most expensive bowler as he conceived 54 runs. Meanwhile, Kuldeep Yadav picked up two wickets, while Khaleel Ahmed and Bhuvneshwar Kumar took a piece each.