New Zealand extended their lead to a commanding 301 after spinner Mitchell Santner took 7-53 to bowl out India cheaply on day two of the second Test on Friday.
India fell to 156 all out, giving the visitors a lead of 103 on a turning pitch in Pune at the end of the first innings.
New Zealand, who lead the three-match series 1-0, were 198-5 at stumps in their second knock after skipper Tom Latham made 86.
Wicketkeeper Tom Blundell, on 30, and Glenn Phillips, on nine, were batting at close of play to raise New Zealand hopes of a first-ever Test series win in India.
Spinner Washington Sundar grabbed four wickets to take his match tally to 11 after returning figures of 7-59 against the Kiwis on day one.
Sundar trapped Devon Conway lbw for 17 in New Zealand's second innings before senior spinner Ravichandran Ashwin sent back Will Young for 23 before tea.
Sundar also bowled Rachin Ravindra for nine as the left-hander attempted a cut only to miss and the skidding ball hit the off stump. Daryl Mitchell soon fell for 18.
Latham reached his fifty in a 60-run partnership with Blundell until his departure when Sundar trapped the left-hander lbw.
Santner sparkled for New Zealand with his left-arm spin as he claimed his first five-wicket haul in 29 Test appearances to trump India at their own game of spin.
Ravindra Jadeja top-scored with 38 but India's batting fell apart, with the hosts bowled out in the second session in just 45.3 overs.
Overnight batsmen Yashasvi Jaiswal and Shubman Gill started cautiously before Santner struck in the 11th over of the day.
He trapped Gill lbw for 30 with a slider to the right-hander.
The home fans were then stunned into silence when Santner took the prized wicket of Kohli, bowled on a low full toss for one.
Off-spinner Phillips struck on his fourth ball to get the left-handed Jaiswal caught at slip for 30 to leave the hosts on 70-4 and then 83-5 when he bowled Rishabh Pant for 18.
First-match centurion Sarfaraz Khan managed 11 before Santner got him caught at mid-on.
India resumed the day on 16-1 and their batting collapse was the second in the series after they fell to 46 all out in the first Test in Bengaluru for their lowest-ever home total.
Last week's win by New Zealand was their first Test victory on Indian soil since 1988.
After the match, Santner said: “It's a great feeling. To put ourselves in a position to potentially win a Test match over here is pretty cool and the way the guys did it with the bat there, doesn't look easy, and we knew how partnerships were key and we managed to do that today, which was outstanding.”
On his seven-wicket haul, he said: “We spoke before the start of the day about how it was about trying to find the right speed on that wicket. I think it changed as the game went on, the slower one started to spin a bit more, so I just tried to put it in the right area for a long time.”
