Indian cannoned through New Zealand's resistance after tea on the fourth day to post victory by 178 runs in the second test.
The win gives them an unassailable 2-0 lead in the series and takes them to No.1 in the world rankings.
For New Zealand it was their fifth defeat in eight tests this year, a result to sit alongside two wins against Zimbabwe and a draw with South Africa at Durban in The Mystery of the Undryable Turf.
Only the light meters could have saved the visitors in the end, dismissed for 197. Tom Latham anchored the chase with 74 and Luke Ronchi offered pep with 32.
Indian captain Virat Kohli raised his arms to the Kolkata faithful, yearning for their support in the middle session. They responded as the stands bloomed with punters in the afternoon haze. The reaction worked like osmosis on the hosts.
New Zealand entered the final session on 135 for three but India's wicket hunt bore down like a heavy roller on the visitors' hopes of survival.
Through the bowlers barreled, relying on the guile, skill and faith that has cemented them as the better side in this series, and indeed the best in the world. Mohammed Shami, Ravindra Jadeja and Ravichandran Ashwin shared three wickets apiece.
For New Zealand, the significance of their predecessors' efforts to win two tests in 33 appearances in India resonates when you see the attrition faced by the incumbents.
This team has presumably grown a new layer of respect for the men who won at Nagpur in 1969 and Mumbai in 1988.
A chase for 376 to win was generally considered arbitrary. The highest chase in 40 matches and 82 years of tests at the venue is 120-2 by India v South Africa in 2004. The highest fourth innings score was 325-3 by India against West Indies for a draw in 1948.
The visitors lost three wickets for 80 in the middle session after Latham and Martin Guptill reached 55 without loss at lunch. They lost seven wickets for 62 as the day came to a premature close.
Tension reigned throughout, not least because Jadeja was warned by umpire Rod Tucker for running across the pitch in his appeals, particularly after a justified lbw shout against Latham on 62. Kohli argued the case, as has become habit when a decision doesn't go his way, but it's hard to defend the indefensible. More than anything, his pestering appears driven by the fear of the public consequences if his team loses.
Visiting teams to India maximise their sports science know-how and mod-cons but drill down through those layers of preparation and contemplation and the New Zealand batsmen still had to take their raw guard in the Eden Gardens furnace against India's formidable attack. There was no lack of courage but to win or draw many would have needed to tap into unprecedented concentration levels, and all without ill captain Kane Williamson.
Yes, players come to India more regularly for the Premier League, but Twenty20 matches are a limited indication as to whether a player can survive the fatigue of a test. Visitors are oppressed by the humidity in front of the local cacophony which demands success from their heroes.
New Zealand had the best of the opening session. They dismissed India for 263, leaving 63 minutes and 16 overs to advance their cause to lunch. The sapping of energy levels in the heat meant it was crucial the batsmen got into the shade to maximise their rehydration and preserve concentration levels. The New Zealanders were taxed 36 runs, but earned the luxury of heading for shelter within an hour of taking the field.
For India, Wriddhiman Saha completed twin half centuries nursing the Indian tail.
Neil Wagner was left on 99 wickets in his 25th test, meaning he cannot equal Sir Richard Hadlee as the fastest to 100.