India needs five New Zealand wickets to win the second Test and series after dominating day three in Mumbai.
Virat Kohli’s side moved from 69-0 overnight to 276-7 before declaring to leave the Kiwis a nominal 540 to win.
Mayank Agarwal made 62, while left-arm spinner Ajaz Patel – who took 10-119 in the first innings – claimed 4-106.
Ravichandran Ashwin took 3-27, as World Test champions New Zealand closed on 140-5 with Henry Nicholls on 36 and Rachin Ravindra two.
India batted until just before tea, with Cheteshwar Pujara and Shubman Gill both making 47.
The two-Test series is currently level at 0-0, after New Zealand batted the whole of day five to earn a draw in the first game.
New Zealand are the current World Test champions after beating India in the final in Southampton in June.