The 178-run victory not only handed the hosts an unassailable 2-0 series lead, but also allowed them to climb back to the top of the ICC Test rankings chart, replacing Pakistan at the summit.
Local boy Wriddhiman Saha was adjudged Man of the Match for his unconquered 54 and 58 in the two Indian innings at the Eden Gardens.
In the second innings, Indian bowlers managed to stop NZ batsmen at 197 while they were chasing mammoth target of 376, put on board by the Indian batsmen, earlier, with the help few partnerships by the tail enders.
Chasing an improbable 376, New Zealand reached 135-3 at tea with opener Tom Latham (74) scoring his ninth test fifty.
But post-lunch, the in-form Indian spinners ran through the Kiwi batting.
Ravindra Jadeja (3/41) and Mohammad Shami (3/46) were the chief wreckers of New Zealand's second innings. Shami took important 3 wickets, while Kumar took one. It should, however, not take anything away from the lower-order batsmen who absorbed the pressure and adapted well on a track that yielded uneven bounce and aided spinners and pacers alike on all four days.
Mitchell Santner (9) and B.J. Watling (1) followed suit in quick succession, Shami accounting for both the scalps.
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Besides Latham, Luke Ronchi was the only one to play an innings of significance, accounting for 32 runs (60 balls, 4x4). Jeetan Patel (2) failed to replicate his first innings form, when he scored a gutsy 47, failing to comprehend the reverse swing generated from a good length ball by Buvneshwar.
Trent Boult was the last wicket to fall on the fourth day when he tried to pull a bouncer but instead top-edged to Murali Vijay, who completed a clean catch.
Kohli's side had entered the series against New Zealand trailing Pakistan by one point and needed to win the series to reclaim the number one position for the fourth time since the current rankings system was introduced in 2003.
Latham continued his vigilant approach and was given good support by Henry Nicholls (24), with whom he shared a 49-run stand.
With the wicket offering a lot of turn, Jadeja made the most of it.
Jadeja claimed Nicholls's wicket after his angled delivery caught the edge of the New Zealander's bat for an easy catch in the slips. Taylor played the wrong line leaving umpire Richard Kettleborough with an easy decision to make as the ball hit Taylor's front pad.
4 Wriddhiman Saha became the first wicketkeeper to score two fifties in a Test at Eden Gardens since 1951. This is their best run in 12 consecutive home Tests; they also had 11 wins out of 12 between January 1988 and February 1994, and between November 1988 and November 1994, but they lost the one other Test, against New Zealand in Mumbai.