Virat Kohli's men wrapped up the series-deciding victory on the Fourth day of the match after setting the Black Caps a mammoth target of 376 runs to chase.
The visitors showed some spark to start with but their chase floundered in the post-tea session and the side was bowled out for 197 in 81.1 overs in what was India's 250th home Test.
The home team had earlier finished its second innings at 263 in 76.5 overs.
Following Rohit Sharma's 82-run knock on Sunday (yesterday), Wriddhiman Saha also picked up his second successive half-century of the match by scoring a 120-ball 58, laced with half a dozen fours.
Faced with an improbable chase, New Zealand were off to a confident start before things went downhill in the final session of the day.
Opener Tom Latham top-scored for them with a 148-ball 74, which included eight hits to the fence.
His innings gave New Zealand some hope of springing a surprise but off-spinner Ravichandran Ashwin put paid to any such eventuality in just the second over after tea, inducing an edge off his bat which was comfortably taken by wicketkeeper Wriddhiman Saha.
Besides Latham, Luke Ronchi was the only one to play an innings of significance, accounting for 32 runs (60 balls, 4x4). However, rest of the Black Caps' line-up failed to apply itself on the tricky track, exploited well by both the pacers and spinners.
Ashwin and Ravindra Jadeja were the top Indian wicket-takers with hauls of 3/82 and 3/41 respectively. Among the pacers, Mohammed Shami grabbed 3/46 in a fine concerted bowling performance.
The two teams will now move to Indore for the third Test starting October 8 which would be followed by a five-match ODI series.
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