Following a top-order wobble, captain Hardik Pandya (15 not out) and Suryakumar Yadav (26 not out) combined for a crucial 31-run partnership as they helped the hosts reach 101-4 on the penultimate ball, chasing New Zealand's 99-8.
Spinners Ish Sodhi and Michael Bracewell picked up a wicket apiece, while Indian batters Ishan Kishan and Washington Sundar were both run out.
New Zealand had posted a strong total of 176 in the first game on Friday, but were unable to repeat that on a pitch that offered plenty of turn, and India's bowlers put them under pressure throughout the innings.
Five Indian bowlers picked up a wicket before Arshdeep Singh dismissed Sodhi and Lockie Ferguson.
The third and final T20I of the series will take place in Ahmedabad on Wednesday.
