New Zealand bowled India out for 462 on day four before bad light stopped play on Saturday four balls into their chase.
The Kiwi bowlers struck late on day four with Matt Henry taking three for 102 and Will O'Rourke three for 92.
The pair have taken 15 of the 20 Indian wickets in the Test so far.
Tom Latham and Devon Conway were yet to score in New Zealand's second innings when bad light stopped play.
The Black Caps haven't won a Test in India since 1988.
Sarfaraz Khan hit 150 and Rishabh Pant 99 for India as they looked to pull off one of the most famous victories in cricket after being dismissed for just 46 in their first innings.
That pair guided India into the lead with just three second-innings wickets down but the hosts lost 7 for 54 with the second new ball to set New Zealand 107 to win.
"I wouldn't say it's an easy wicket here. Obviously, we've got a world-class team going up against us," O'Rourke said.
"We've got to be confident going out there tomorrow and hopefully for the crowd's sake the rain stays away and we get the chance to have a crack at the total."
Safaraz said: "It is not an easy wicket and I feel the game has not slipped out of our hands. If we can take out two or three quick wickets then they will suffer the same fate."
After the first day was washed out, India's first innings 46 on day two was the third-lowest total in their Test history and lowest at home.
