New Zealand opener Tom Latham soldiered on but the Indian spinners made vital inroads in the second session on the fourth day of the second test to reduce the touring side to 135 for three wickets on Monday.
At tea, Latham (74) and Luke Ronchi (nine) were unbeaten at the crease for New Zealand who still need 241 runs for a series-levelling victory. In the 53rd over, Ashwin drew Latham forward, ball edged through to Wriddhiman Saha behind the wicket sending Latham back to pavilion.
Set a target of 376, Latham and Martin Guptill (24) survived some nervous moments before lunch to give New Zealand a solid start in their chase with a series-best opening stand of 55.
Guptill, whose place in the test side is under scrutiny after a string of poor scores, was on six when he was given not out on a confident appeal for leg before against paceman Mohammed Shami.
The right-hander was out leg before in the first over after the lunch break to off-spinner Ravichandran Ashwin, who also sent back New Zealand's 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 got an edge to slip off Ravindra Jadeja, whose strong leg before appeal against Latham was turned down.
Earlier resuming on 227 for eight, India were all out for 263 in their second innings, setting New Zealand a difficult target on a much deteriorated track.
Wriddhiman Saha was not out on 58, his second unbeaten fifty of the test, with the hosts looking to take an unassailable 2-0 lead in the three-match series and reclaim the top spot in the world test rankings from Pakistan.
Trent Boult, Matt Henry and Mitchell Santner picked up three wickets each for the touring side.
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 "Cricket, India v/s New Zealand, Tom Latham, Martin Guptill, R Ashwin, Wriddhiman Saha, Kane Williamson, Luke Ronchi, Mitchell Sa")
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