India crushed New Zealand by 178 runs in the second Test on Monday to clinch the three-match series and reclaim top spot in the world rankings from Pakistan.
Chasing 376 for victory, the touring side were bundled out for 197 in fading light on the fourth day at Eden Gardens to give India an unassailable 2-0 lead in the series.
India will return to the top of the International Cricket Council Test rankings irrespective of the result of the third and final Test in Indore which starts on Saturday.
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New Zealand opener Tom Latham waged a lone battle, top- scoring for his side with a dogged 74.
Latham and Martin Guptill (24) survived nervous moments before lunch to give New Zealand a solid start with a series-best opening stand of 55.
Guptill, whose place in the side is under scrutiny after a string of poor scores, was on six when he was given not out following a confident appeal for lbw by Shami.
The right-hander was trapped leg before in the first over after lunch by off-spinner Ashwin, who also sent back stand-in skipper Ross Taylor (four) in similar fashion.
Latham concentrated hard to bring up his second half-century of the series and added 49 for the second wicket with Henry Nicholls (24), who replaced regular captain Kane Williamson in the side.
Nicholls edged Jadeja to slip before Shami picked up two quick wickets by getting the ball to reverse swing and New Zealand lost seven wickets in the final session.
Local boy Shami returned to take the final wicket of Trent Boult much to the delight of the crowd.
Earlier, resuming on 227 for eight, India were all out for 263 in their second innings, setting New Zealand a difficult target on a wearing track.
Wriddhiman Saha was not out on 58, his second unbeaten fifty of the match.
Boult, Matt Henry and Mitchell Santner picked up three wickets each for the touring side.