The 37-year-old batting maestro, who had scored 376 in his last four ODI innings, anchored India's chase of 301 with a sublime knock of 93 featuring eight boundaries and a six, but he was dismissed by Kyle Jamieson when a landmark century was within reach.
The Vadodara crowd's disappointment was palpable as their hero departed, but they rose to applaud Kohli, who achieved another milestone by becoming the second-highest run scorer in international cricket across all formats.
With his 77th ODI fifty, Kohli moved on to 28,068 runs and surpassed Sri Lankan great Kumar Sangakkara (28,016) to sit behind only Indian icon Sachin Tendulkar's 34,357.
Conway and Nicholls start well
Earlier, India won the toss and elected to field, factoring in dew conditions for the second innings, but New Zealand's openers Devon Conway (56) and Henry Nicholls (62) frustrated the hosts with a commanding 117-run opening stand.
Harshit Rana provided the breakthrough, striking twice in consecutive overs to dismiss both openers and apply the brakes on New Zealand's scoring rate.
The middle order failed to capitalise on promising starts, with only Daryl Mitchell making a significant contribution, while skipper Michael Bracewell was run out from a direct hit by Shreyas Iyer.
Mitchell blazed his way to 84 with five boundaries and three sixes before being trapped leg-before to Prasidh Krishna while attempting another big shot. Kristian Clarke's unbeaten 24 helped New Zealand add 50 runs in the final five overs to reach 300.
Kohli and Gill pile on the runs
India's chase got off to a rocky start when opener Rohit Sharma fell for 26, but Kohli and captain Shubman Gill steadied the ship with a crucial 118-run partnership. Gill contributed a patient 56 but fell shortly after receiving treatment on his back.
Jamieson (4-41) then turned the match on its head with a devastating spell, removing Ravindra Jadeja in the same over as Kohli before clean-bowling Iyer for 49, his off stump knocked out of the ground as India slumped to 242-5.
Enter Rana, who counter-attacked brilliantly and was fortunate to survive a dropped catch at long-on when on 12. He made New Zealand pay, scoring 29 before being caught behind, keeping India in the hunt.
With pressure mounting and India needing to maintain a run-a-ball rate, KL Rahul held his nerve to guide the hosts home with an unbeaten 29, sealing victory with two fours and a six in the penultimate over.
The victory gives India a 1-0 lead in the series ahead of the second game in Rajkot on Wednesday.