India chased down the target with 10 balls to spare, riding on Kohli's 26th century in the 50-over format.
The hosts lost both their openers Rohit Sharma and Ajinkya Rahane inside nine overs and, with the required run rate climbing, needed a solid partnership to get back on track.
Kohli, who was dropped on six by Ross Taylor off Matt Henry, and Dhoni (80), who promoted himself up the batting order to number four, provided just that with a brisk third-wicket stand of 151 runs.
India's test captain Kohli, who will turn 28 next month, finished things off with an unbroken fourth-wicket stand of 97 with Manish Pandey (28 not out).
With India needing 23 from 18 balls, the stylish right-handed batsman, who scored an unbeaten 85 in the first ODI, tore into paceman Trent Boult, hitting three fours and a six in his over to plunder 22 runs.
Earlier, James Neesham (57) and Matt Henry (39 not out) added 84 for the ninth wicket to prop up New Zealand after the touring side had been reduced to 199 for eight following a middle-order collapse.
Opener Tom Latham top-scored for New Zealand with a 61 and the side were comfortably placed at 153 for two in the 29th over with a promising stand of 73 between Latham and Taylor (44).
But they lost their next six wickets for 46 runs needing some rearguard action from Neesham and Henry.
Paceman Umesh Yadav and off-spinner Kedar Jadhav each picked up three wickets for the hosts though the former proved expensive, giving away 75 runs in his 10 overs.
The fourth ODI will be played in Ranchi on Wednesday.
(Reporting by Sudipto Ganguly in Mumbai; Editing by Clare Fallon)
