A consecutive century by Ross Taylor powered the hosts to 303/5 in their 50 overs after being put in to bat. But the visitors could only manage 216 and were bowled out with two balls to spare. Pacer Matt Henry impressed on debut, taking 4/38 in 10 overs.
The loss meant India lost their second overseas series in a row after going down in South Africa.
The hosts struggled at the start against pacers Mohammed Shami (1/61) and Bhuvneshwar Kumar (1/48). But New Zealand came back strongly, backed by a 152-run third-wicket partnership between Kane Williamson (88) and Taylor (102) which took them beyond the 300-mark.
In Image: New Zealand cricket players celebrate their series victory over India