Ambati Rayudu led a middle-order recovery before New Zealand struggled with the bat as India earned a 35-run win in the fifth and final ODI.
India had already sealed the series but had been humbled in an eight-wicket defeat in the fourth contest, in which they were bowled out for a measly 92.
A similar scenario appeared to be playing out when India, who had opted to bat despite moisture on the Wellington surface, slipped to 4-18.
However, Rayudu mixed scratchy defence with some fine stroke play to make a crucial 90, while all-rounders Vijay Shankar and Hardik Pandya (both 45) contributed to India's 252 all out.
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The Black Caps were always playing catch-up in reply and Mohammed Shami (2-35), Pandya (2-50) and Yuzvendra Chahal (3-41) ensured wickets fell at regular intervals as New Zealand were bowled for 217.
Rohit Sharma, standing in as captain for Virat Kohli, asked India to challenge themselves in testing conditions after opting to bat on a pitch more suited to bowling.
India toiled at first as Sharma (2), Shikhar Dhawan (6), Shubman Gill (7) and MS Dhoni (1) fell inside 10 overs, with Trent Boult (3-39) and Matt Henry (4-35) claiming a couple of wickets each.
Rayudu and Shankar put on 98 for the fifth wicket, though, the latter at first looking more at ease before his 64-ball knock was ended by a run-out following a miscommunication.
It took Rayudu a while to get going but a six over the long-on boundary off Colin de Grandhomme laid the foundation for a more fluent showing and he whacked Colin Munro for six on three occasions.
Rayudu scored 46 off his final 31 balls before a slice off Henry to cover saw him fall short of a century.
Pandya enjoyed an electric 22-ball showing that included three consecutive sixes, the fifth time he has done so in his career, to dent Todd Astle's (0-35) figures and lift India's total.
New Zealand never truly got going in reply with Shami accounting for openers Henry Nicholls (8) and Munro (24) and Ross Taylor (1) facing just four deliveries before being trapped lbw by Pandya.
Dangerman Kane Williamson (39) put on 67 with Tom Latham (37), but when he undercooked a Kedar Jadhav delivery to deep midwicket the momentum was stalled.
Chahal then trapped Latham and quickly snared De Grandhomme (11) and, despite a gutsy 44 from Josh Neesham and Mitchell Santner's 22, New Zealand had too much ground to make up.