Kohli and Dhoni combined well and notched a 95-run stand for the fifth wicket, taking India closer to the target.
With Stuart Binny knocking on the doors, Ravindra Jadeja (0) didn't do himself any favours with a dismal show with the bat.
Kohli hit a few lusty blows to keep India's hopes alive but his fall in the 45th over ended all chances of an Indian win.
Some clean hitting by Ravichandran Ashwin (12) and Mohammad Shami(7 not out) managed to take India close but it was never enough.
Earlier, after losing openers Martin Guptill (8) and Jesse Ryder (18) cheaply, Kane Williamson crafted the innings initially, stroking his way to 71 off 88 balls, guiding New Zealand to safety.
Mohammad Shami, on his first tour to New Zealand, bowled brilliantly, removing both openers before dismissing the dangerous Ross Taylor and Nathan McCullum (2).
Williamson, along with former captain Ross Taylor (55), steadied the ship with a patient 121-run stand for the third wicket.
