New Zealand were put into put and had slipped to 58-3 before the match-changing partnership between Mitchell and Phillips, who added 219 from 188 balls.
Mitchell, who made 84 in the first match of the series and 131 in the second, hit 15 fours and three sixes for a career-high ODI score.
His fourth-wicket partnership with Phillips came to an end when the latter was caught behind off Arshdeep Singh.
Mitchell was removed soon after by Mohammed Siraj, but an unbeaten 28 from captain Michael Bracewell helped the Black Caps pose an imposing 337.
Kohli, who now only plays the 50-over format having retired from Test and T20 international cricket, hit 10 fours and three sixes in his 108-ball knock, but it was not enough.
These teams next meet in a five-match T20 series starting on 21 January, before the T20 World Cup gets under way on 7 February – co-hosted by India and Sri Lanka.