Tom Blundell was unbeaten on 30 and Glenn Phillips was batting on nine as the Black Caps, who won the series opener by eight wickets, extended their lead to 301 runs at the close after scoring 259 in the first innings.
"It's a great feeling but to put ourselves in a position to potentially win a test here is pretty cool," Santner said.
"The way the guys did it with the bat there, it doesn't look easy and we knew getting partnerships was the key. We managed to do that today, which was outstanding."
Washington Sundar got rid of Devon Conway for 17, Rachin Ravindra for nine and Daryl Mitchell for 18 while Ravichandran Ashwin dismissed Will Young for 23, but the runs came quickly and too easily for New Zealand.
Lunch on Day 2 of the Pune test! #TeamIndia 107/7 at the end of First Session.
— BCCI (@BCCI) October 25, 2024
The Second Session to commence soon.
Scorecard ▶️ https://t.co/YVjSnKCtlI #INDvNZ | @IDFCFIRSTBank pic.twitter.com/5ZZx1Ovm37
New skipper Tom Latham returned to form with a timely 86 but became Washington's fourth victim late in the afternoon after he put the tourists in a strong position to secure their maiden series victory in India.
India are seeking a 19th straight home series victory since a 2-1 defeat by England in 2012, but will need a battling effort to draw level with New Zealand ahead of the finale in Mumbai early next month.
Santner had earlier posted career-best figures of 7-53 while Phillips bagged 2-26 as the spinners continued to sparkle at the Maharashtra Cricket Association Stadium, where Washington took 7-59 on the first day.
The hosts resumed on 16-1 after losing captain Rohit Sharma for a nine-ball duck, and Shubman Gill was fortunate to survive a loud appeal for lbw on the third ball of the morning from Santner when he was on 10.
Back in the side after missing the series-opening defeat in Bengaluru due to a stiff neck, Gill shrugged off the early scare and went on the attack by lofting paceman Tim Southee for a six.
QUICK STRIKES
Santner trapped Gill plumb in front for 30 and the left-armer struck again by bowling out Virat Kohli for one with an inviting full toss that the batsman missed completely, as two quick strikes rattled India.
"We tried to find the right speed on that wicket. It changed as the game went on," Santner added.
"The slower ones started to spin a bit more and we tried to put it in the right areas. Got a little bit greedy later on with the changes of pace, but it was nice to see it spin.
"We don't get to hear that back home. So as a spin unit, when we come here, we know it's always a challenge but it can offer assistance which is nice."
Yashasvi Jaiswal drove and swept the bowlers and appeared a lot more at ease at the other end, although the left-hander was lucky his slog sweep off Ajaz Patel fell in no man's land when he was on 16.
Mitchell pulled off a sharp catch at slip as Phillips dismissed Jaiswal for 30 and the tourists could have had another had the fielder held onto a tough chance when Santner forced an edge off Sarfaraz Khan's blade.
Rishabh Pant was castled for 18 by Phillips after a loose shot and Santner had Sarfaraz caught for 11 to leave India on the ropes at 95-6, with both their batting heroes from the opening game back in the dugout.
Santner trapped Ashwin lbw for four and removed Ravindra Jadeja in similar fashion after the batsman made a defiant 38, before getting one to go through Akash Deep's defence.
He then snared Jasprit Bumrah for a duck to ensure that New Zealand would begin their second innings with a lead of 103 runs.
Mitchell Santner and Glenn Phillips run through India's batting in Pune.#WTC25 | #INDvNZ 📝: https://t.co/f0g4C3OkUV pic.twitter.com/t6kxv4mIMc
— ICC (@ICC) October 25, 2024
INDIA: Rohit Sharma (capt), Yashasvi Jaiswal, Shubman Gill, Virat Kohli, Sarfaraz Khan, Rishabh Pant (wkt), Ravindra Jadeja, Washington Sundar, Ravichandran Ashwin, Akash Deep, Jasprit Bumrah
NEW ZEALAND: Tom Latham (capt), Devon Conway, Will Young, Rachin Ravindra, Daryl Mitchell, Tom Blundell (wkt), Glenn Phillips, Mitchell Santner, Tim Southee, Ajaz Patel, William O'Rourke