Defending a modest 209 in Tauranga on Sunday, India looked destined for defeat and a 2-2 drawn series as New Zealand cruised to 1-64 before the visitors' quicks sparked a dramatic collapse.
The hosts lost 5-55 before crashing out for 187 in 48.1 overs as India won the series 3-1, with game three abandoned due to rain.
Put in to bat, India made a cautious start, mindful of their crushing 244-run defeat in the previous ODI.
But their approach unravelled as New Zealand's bowlers ripped through the top order before Axar Patel and Ishan Kishan helped the visitors recover to make 209 in 42.1 overs.
New Zealand openers Will Young and Nick Kelly capitalised on the platform laid by their bowlers and looked on course for a comfortable chase before India's bowlers breathed life into the contest in the middle overs.
Yash Thakur built pressure with a disciplined spell, while Mohammed Siraj and Arshdeep struck at regular intervals as the hosts slumped from 1-64 to 6-119.
Dean Foxcroft top-scored with 31 off 42 balls and attempted to steady the innings as wickets tumbled around him, but Yash removed him to claim his maiden ODI wicket.
Captain Mitchell Santner's 24 off 31 balls offered resistance, but India's bowlers continued to chip away and eventually wrapped up the tail to complete a memorable victory.
Arshdeep finished with 3-30 off 10 overs, while Siraj and spinner Patel picked up two wickets apiece and the remaining bowlers claimed one each.
Earlier, New Zealand's attack kept India on the back foot throughout, with fast bowler Matthew Fisher striking early to remove veterans Rohit Sharma and Virat Kohli.
Patel, who survived two chances, stitched together a 52-run partnership with Shreyas Iyer (22) before combining with Kishan in a bid to rebuild the innings.
Patel and Kishan scored 46 apiece, while Naman Dhir contributed a late 22 before Jacob Duffy and Santner wrapped up the tail.
Santner (3-47) and Duffy (3-60) claimed three wickets each, while Fisher finished with two.
India captain Shreyas Iyer was delighted to seal both white ball contests, after India won the T20 series 3-2.
"I think in both the T20 and ODI series we were confronted with different conditions, the weather kept changing, we were faced with a lot of challenges and coming out on top is a great achievement," Iyer said.
"Although we didn't get as many runs as we wanted, we still believed we could change the game at any point. I'm glad that each individual thought in the same direction."
