Skipper Rohit Sharma (76) topscored for India, who chased down the 252-run target with one over to go.
Daryl Mitchell made 63 and Michael Bracewell contributed an unbeaten 53 down the order to help New Zealand post a competitive 251-7 after electing to bat.
India's four-pronged spin attack kept the run rate in check but they did not get enough support from the fielders, who dropped four catches.
India nearly squandered a strong start but KL Rahul chipped in with an unbeaten 34 down the order to help them complete a successful chase.
More to follow...