The hosts were all-out for 217 runs. Yuzvendra Chahal clinched three wickets, while Mohammed Shami and Hardik Pandya took two apiece in the fifth ODI.
India's bowlers rattled New Zealand's batsmen to win the fifth and final ODI by 35 runs at the Westpac Stadium, Wellington. That also meant they won the ODI series 4-1, having lost the fourth ODI at Hamilton by eight wickets.
Yuzvendra Chahal clinched three wickets, while Mohammed Shami and Hardik Pandya took two apiece. Pacer Bhuvneshwar Kumar and right-arm off-break spinner Kedar Jadhav got one wicket each.
It was Jadhav who got Australian skipper Kane Williamson's wicket. Jadhav bowled a low one; Williamson heaved but ended up caught by Shikhar Dhawan near the boundary line.
Shami provided India with the breakthrough in the fourth over to dismiss opener Henry Nicholls as the hosts chased a target of 253 runs. Shami struck again to clean bowl Colin Munro for 24 runs.
Opting to bat, Ambati Rayadu's patient 90 and Hardik Pandya's 45-run cameo powered India to a decent 252 total. Pandya faced just 22 balls to hit 45 runs which included two boundaries and five sixes. He was caught out while trying to hit a six.
Rayudu, meanwhile, slammed a crucial half-century to lift India after early strikes. The batsman was going strong against the New Zealand attack was also dismissed while trying to hit a big shot.
India's current no 4 was sent back to the pavilion 10 runs short to his century which included eight boundaries and four sixes.
Earlier, Rayudu and Vijay Shankar revived Indian innings after the visitors lost four wickets for just 18 runs in the fifth and final ODI against New Zealand on Saturday. The partnership, however, ended after Shankar was run-out for 45.
Relying on skipper MS Dhoni, who returned to the squad after missing two ODIs due to injury, was clean bowled. He faced a total of six balls and made just one run.
For New Zealand, James Neesham top-scored for his side but was run-out in the most unexpected but brilliant way by wicketkeeper-batsman MS Dhoni.
Apart from Neesham, skipper Kane Williamson and Tom Latham managed to cross the 30-digit mark. The two scored 39 and 37 runs respectively. In bowling, Matt Henry clinched four wickets while Trent Boult grabbed three to dominate India initially.
After clinching the ODI series, India will lock horns with New Zealand in the T20 series, with the first being played on February 6.