New Zealand were always going to do well to manage anything more than delaying the Indian celebrations when they resumed on 93 for four in their pursuit of an improbable 434-run victory target on a track offering generous spin and bounce.
To their credit, they kept the home bowlers at bay for 50 overs on a turning day-five track before collapsing for 236 to give the hosts a comprehensive victory in the milestone test.
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Ravichandran Ashwin claimed 6-132 to complete his 10-wicket match haul and prove why he is considered India's premier spinner.
"The boys applied themselves well, there were a few moments where we were in a spot of bother," said India skipper Virat Kohli. "It's been a memorable test match and exciting to play. They [New Zealand] showed some resistance and that's what you want in a test match. I'm sure the series is going to get more and more competitive as it goes on."
When final day's play began under an overcast sky, overnight batsmen Luke Ronchi (80) and Mitchell Santner (71) continued their resistance against the in-form Indian spinners at Kanpur's Green Park Stadium.
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Kohli predictably began with spin from both ends, but the batsmen mixed caution with aggression to defy their hosts.
Left-arm spinner Ravindra Jadeja finally made the breakthrough when he induced Ronchi into an ill-timed slog against the turn and Ashwin pouched the skier at point.
The dismissal pretty much summed up a test in which India's spin duo, who shared 16 of the 20 Black Cap wickets between them, combined to wreck New Zealand's hopes of a result.
It was a tame end to Ronchi's 102-run partnership with Santner, a defiant battle spread over 36 overs that proved the local spinners were not unplayable. Ronchi hit nine boundaries and a six before his rush of blood to the head ended his inning.
In a match dominated by the spinners, Mohammed Shami also displayed his reverse swing mastery and got one to jag back into BJ Watling's pad before he uprooted Mark Craig's middle stump with another swinging delivery. Craig will now return home to recover from a side strain. He was replaced in the squad by Jeetan Patel.
Santner completed his fifty but was then served a nearly unplayable ball from Ashwin, which pitched way outside the leg-stump, turned and bounced viciously to kiss the shoulder of the bat and nestle in Rohit Sharma's waiting hands at silly point.
The off-spinner then trapped Neil Wagner leg before to seal the victory. Kolkata hosts the second of the three tests from Friday.
"There were a lot of positives we'll take into the next test, hopefully a few lessons as well," said New Zealand captain Kane Williamson. "Credit goes to India, they outplayed us with bat and ball. It was a combination of many things but there is no doubt that India was the better team.”
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