The veteran right-hander hit his 80th ODI fifty off just 35 balls, showing his enduring class on a night when no other batsman was able to flourish.
In a rain-affected match, India chased down a reduced 143 for victory with 56 balls remaining after New Zealand stuttered to 185 all out in the first innings, taking a 1-0 lead in the five-game series.
Kohli, who turns 38 on Thursday, strode to the middle at the end of the first over, after former captain Rohit Sharma departed for a duck.
He immediately found his timing on a quick and bouncy wicket, playing a stunning array of pulls and hooks which left New Zealand's pace attack flummoxed.
Kohli hit 13 fours and a six in his 51-ball stay, frequently attacking the short ball.
Indian captain Shubman Gill and Kohli combined for a 113-run partnership, Gill adding 37 from 56 deliveries.
Rain interrupted the chase in the 11th over, when India were at 54-1, and then again an over later at the end of the 12th, with the tourists having added a further 10 runs.
When they returned a third time, India were targeting a total of 143 runs in 32 overs under Duckworth Lewis -- that is, a further 79 runs in 20 overs.
Kohli hit double digits from the next three overs to effectively kill the chase.
Jacob Duffy took three wickets for New Zealand.
India won the toss and chose to field, after brief showers caused a 10-minute delay to the start.
New Zealand steadily reached 73-2 in the 14th over despite Will Young and Henry Nicholls both falling cheaply.
Tim Seifert, playing in place of Devon Conway after he was concussed in a freak collision with Matt Henry in training on Tuesday, departed for 38, mistiming a pull shot to mid-on.
His would be the highest score for New Zealand, with Daryl Mitchell's 28 and Glenn Phillips's 30 the next-best scores until a blistering 34 from 23 balls by last man Blair Tickner.
Arshdeep Singh took 4-70 from his 10 overs, while Gurnoor Brar had 3-44 in 9.2 overs, as New Zealand were bowled out for 185 in the 41st over.
The second game of the five-match series is in Wellington on Saturday.