Only three New Zealand batsmen could reach double figures with the visiting captain Kane Williamson top-scoring with 27 as his side were bundled out in just 23.1 overs for their lowest ODI score against India.
Williamson's dismissal to Axar Patel, who took two wickets for nine, triggered a collapse which saw New Zealand lose their last seven wickets for 16 runs with Mishra bagging five of them.
The 33-year-old fooled the batsmen with his flight and sharp turn and also extracted some extra bounce on the surface during his six overs.
Mishra (5-18) was adjudged man of the match and also the player of the series for picking up 15 wickets in the five matches.
Earlier, Rohit and Kohli gave India the momentum with a 79-run stand for the second wicket before the former was out on 70 in the 22nd over.
Kohli, who had already scored 85 not out and an unbeaten 154 in the series, kept India's innings moving briskly with a 71-run stand with Dhoni but his dismissal for 65 triggered a mini-collapse for the hosts.
Dhoni and Manish Pandey were also soon back in the pavilion and India were reduced from 190-2 to 220-5 in quick time.
Kedar Jadhav's unbeaten 39 and Patel's 24 gave India, who also blanked New Zealand 3-0 in the tests, the late surge with a sixth-wicket partnership of 46.
(Reporting by Sudipto Ganguly in Mumbai; editing by Clare Fallon)
