Santner heroics seal historic New Zealand Test series win in India
The visitors bowled out India for 245 in their chase of 359 on day three to take an unbeatable 2-0 lead in the three-match series.
It is India's first Test series defeat at home since December 2012, when Alastair Cook's England beat them 2-1.
Before now New Zealand had never won a Test series on Indian soil dating back to 1955 and the Black Caps celebrated to stunned silence.
"Immensely proud to be in a position of winning two Test matches here. Proud of the group," skipper Tom Latham said of his history-makers.
"Lot of New Zealand teams have come over the past 69 years and 13 series, and to be the first team to win a series here is special."
Santner, whose 7-53 in India's first innings of 156 set up the famous win, rattled the Indian chase with six wickets on a turning pitch and trumped the hosts at their own spin game.
"Every time you take wickets you get a little more confident," player of the match Santner said.
"I felt that today. Every time I got a wicket, it got a little better."
The left-hander bowled unchanged from one end, returning figures of 6-104 in 29 overs.
Ajaz Patel took the final two wickets and ended Ravindra Jadeja's resistance on 42 when the batsman holed out in the deep.
With the series defeat, India's record of 18 consecutive bilateral home series wins -- the longest such run for any team -- came to an end.
"I don't think we batted well enough to get runs on the board," India skipper Rohit Sharma said.
"It is a collective failure. The team has failed to accept the challenge thrown at us."
Rohit hurting
Rohit, whose side travels to Australia for a five-Test series starting next month, added: "We lost the game and the series, that is hurting.
"But we won 18 series in India and that means we did a lot of good things (in the past). I will not think too much into this.
"We had two-three bad innings, but it happens sometimes."
India's famed batting has flopped twice in the series including getting bowled out for 46 for their lowest total at home in the opener in Bengaluru.
India still lead the World Test Championship table but Australia are a close second.
India bowled out New Zealand for 255 inside the first hour of play and opener Yashasvi Jaiswal in his 65-ball 77 came out attacking to raise hopes of a miracle.
The hosts lost Rohit for eight but raced to 81-1 at lunch in 12 overs.
Santner took down Shubman Gill for 23 soon after the break to end a 62-run second-wicket stand with the left-handed Jaiswal, who powered on after reaching his fifty.
The in-form spinner finally had Jaiswal caught at slip, then ran out Rishabh Pant for a duck and trapped Virat Kohli lbw, dousing India's remote chances.
Glenn Phillips chipped in with the wicket of Washington Sundar for 21.
India spinners Sundar and Jadeja shared seven wickets between them in the second New Zealand innings, with Jadeja claiming three of the five to fall on Saturday morning.
Sundar, a lanky off-spinner, returned to the Indian Test team after more than three years and took 7-59.
New Zealand made 259 in their first innings riding on knocks from Devon Conway (76) and Rachin Ravindra (65) before Santner took charge.
New Zealand have now won four Tests in India after their opening triumph, which marked their first on Indian soil since 1988.
The series victory comes after New Zealand's recent 2-0 loss in Sri Lanka on a sub-continent tour that began with a washed-out Test against Afghanistan near New Delhi.
Tim Southee stepped down after the Sri Lanka defeat and Latham took over as Test captain.
The final match starts November 1 at Mumbai's Wankhede Stadium.