Kanpur: India need another six wickets to win the first Test as New Zealand, chasing 434 runs for victory, were precariously placed at 93 for four at stumps on Sunday.
Off-spinner Ravichandran Ashwin claimed three wickets in Kanpur to dent the visitors' chances on the fourth day, as India seek to go one up in the three-match series.
New Zealand, who need 434 runs to win the first Test at Green Park, will have a tough final day if they are to even manage a draw as the visitors' have already lost four wickets for 93 runs.
Kohli decided to open the bowling with Mohammed Shami and Ashwin, with the latter starting brilliantly.
After Ashwin dismissed Martin Guptill and Tom Latham in the fourth over, it was always going to be difficult for the New Zealand batsmen.
Skipper Kane Williamson handled Ashwin decently, and scored some important runs, but the off-spinner's brilliance was too much for the right-hander, who was trapped leg before. Williamson, thus, became Ashwin's 200 Test victim as well.
The Black Caps were in further trouble as Taylor was run out by Umesh Yadav as well.
Earlier, India set New Zealand a daunting victory target of 434, after declaring their second innings on 377 for five on the fourth day.
Rohit Sharma (68) and Ravindra Jadeja (50) stitched together an unbeaten 100 for the sixth wicket, and the umpires called for tea soon after the declaration by the hosts, playing their 500th test.
The duo played attacking cricket in the second session to put India in a strong position. Jadeja hit two fours and three sixes during his 58-ball knock and Sharma struck eight boundaries for his fifth Test fifty.
Cheteshwar Pujara top-scored for the hosts with 78 and his 133-run second-wicket partnership with Murali Vijay (76) was the highlight of the innings.
New Zealand spinners Mitchell Santner and Ish Sodhi claimed two wickets each.
India's own spinners, Ravindra Jadeja and Ravichandran Ashwin, had put the hosts in a commanding position on Saturday after New Zealand were bowled out for 262 in their first innings in response to India's 318.
Jadeja, who recorded his fifth five-wicket haul in Tests, and Ashwin shared nine wickets between them.
Brief scores
India - 318 (Vijay 65, Pujara 62, Boult 3-67, Santner 3-94) and 377/5 dec (Pujara 78, Vijay 76, Rohit 68*, Jadeja 50*)
New Zealand - 262 (Williamson 75, Latham 58, Jadeja 5-73, Ashwin 4-93) and 93/4 (Ronch 38, Ashwin 3-68)
Status - New Zealand need 341 runs to win