''It was a fantastic partnership which took the game away from us."
India needed 23 off the last three overs but left armer Trent Boult was flayed for 22 in the 48th over to seal the win.
''We may have given a bit too much to New Zealand, but we took it as an opportunity to chase them down, because we know we are a good chasing team," Kohli said.
''It wasn't the easiest pitch. Some balls were stopping on us."
Allrounder Jimmy Neesham's maiden ODI half century could scarcely have come at a better time for New Zealand.
Lefthander Neesham revived a sagging New Zealand innings with 57 off 47 balls as part of a record-setting ninth-wicket stand of 84 with seamer Matt Henry, who finished on 39 off 37 balls.
New Zealand, sent in after losing a sixth straight toss on tour, made a flying start with a brace of sixes by opener Martin Guptill.
However from 80 for two in 13 overs, New Zealand lost some momentum but the innings fell apart after Tom Latham and Ross Taylor had put on 73 for the third wicket.
New Zealand lost four for 16 in 21 balls at one point, six for 46 in 57 balls, before Neesham and Henry put a late kick into the innings.
It made depressing viewing as it happened in good batting conditions.
Innocuous offspinner Kedar Jadhav took three for 29 off five overs while legspinner Amit Mishra had both Taylor and Luke Ronchi stumped with fine deliveries.
Sweeping and driving impressively, he had strong support from Henry, who at one point took 14 balls in three successive Umesh Yadav deliveries in the 49th over.
The stand ended in the penultimate over when Neesham skied a catch to deep cover. It suggested New Zealand have hidden strength with eight wickets down. At Dharamsala in the opening ODI, Latham and Southee put on 71 for the ninth wicket.
"Obviously it was frustrating to lose those wickets in the middle in a clump, we were probably looking at a bit more at that stage," Williamson said.
''But the lower-order performed really well. Neesham and Henry were outstanding.
''To lose those wickets and end up on 280, we were pleased. Maybe we wanted more, but with early wickets we could have made it harder."
Kohli had a big slice of good fortune in the fifth over of India's chase, when he was dropped by Taylor at wide slip.
Kohli had glanced a ball from Henry towards third man but didn't take account of Taylor's placement. The ball flew low to Taylor, he got both hands to the ball but dropped it.
''A bit of luck went my way. I feel sorry for Ross," Kohli said.
''It's never easy to drop a catch and the batsman carries through. I've done that, and Brendon (McCullum) got 300 in Wellington," he added referring to the innings in which McCullum made 302 at Wellington in 2014.
Williamson accepted the dropped catch as ''part of the game. You want to catch them all, it doesn't always happen."
Dhoni became the most prolific hitter of sixes in ODIs by an Indian, overtaking Sachin Tendulkar's mark. He also went past 9000 ODI runs, the fifth Indian to the feat.
The fourth ODI is at Ranchi on Wednesday.
