Chasing 293 to win, Kohli took India closer with a classy 111-ball 123 but the hosts held their nerve to take 1-0 lead in the five-match series.
Left-handed all-rounder Corey Anderson was the Man-of-the-match for his quick 68 not out and two wickets.
Mohammed Shami was India's successful bowler with four wickets.
Today's ton was Kohli's 18th in ODIs and first time that his hundred failed to give India a win while chasing. Kohli has hit 12 centuries while batting second with 11 previous ones ending in winning cause.
Here are the pictures from the match.
Celebration time for the Delhi youngster
Virat Kohli celebrates his century as captain MS Dhoni watches in Napier.
Indian fans in Napier
Indian fans wave the Tri-colour at the McLean Park stadium in Napier.
Shami gets Ryder bowled
Mohammed Shami exults after dismissing Jesse Ryder bowled.
Ishant has a bad day again
Ishant Sharma was once again expensive with his bowling. He conceded 72 runs for one wicket in 9 overs.
Shami is delighted
Shami is delighted after taking a wicket. He finished with 4/55 in 9 overs.