Santner ended with 6-104 for a match haul of 13 to set up the historic win and it was his senior spin partner Ajaz Patel who picked up the last two Indian wickets, including Ravindra Jadeja for a defiant 42, to settle the contest.
It was a stunning defeat for India, who were dismantled by eight wickets in seamer-friendly conditions in the opening match at Bengaluru, as they suffered their first series loss on home soil since falling to England in 2012.
Their proud run of 18 successive home series wins since that 2-1 humbling was ended by the inspired Black Caps, who were by far the better side in both matches and will target a clean sweep in the finale at Mumbai from Friday.
India's highest successful run chase at home is the 387-4 they scored to beat England in Chennai in 2008 but any hopes of a similar effort faded on the black-soil turner at Maharashtra Cricket Association Stadium where spinners wreaked havoc.
They made a blazing start as Yashasvi Jaiswal smacked some spectacular boundaries, but his dismissal for 77 by Santner and Rishabh Pant's shocking run out for a duck after lunch left India in deep trouble at 127-4.
Santner, who had earlier removed Rohit Sharma for eight and Shubman Gill for 23, continued to torment India as the left-arm spinner trapped trump card Virat Kohli lbw for 17 and set the alarms bells ringing in the home changing room.Sarfaraz Khan was unable to recreate his batting heroics from the opening match, perishing for nine after missing a low delivery from Santner to hand the bowler back-to-back five-wicket hauls.
The shoulders really dropped when Washington Sundar fell for 21 to Glenn Phillips late in the afternoon session, and Santner had Ravichandran Ashwin caught for a solid 18 as India were staring down the barrel at 206-8.
New Zealand were bowled out for 255 in their second innings after skipper Tom Latham's 86 and handy contributions lower down the order put them in a strong position to secure a first-ever series victory in India.
Resuming on 198-5 with their lead already at more than 300 runs on an increasingly tough pitch, New Zealand trotted along nicely in the morning until Jadeja castled Tom Blundell for 41 for his first wicket of the match.Santner, who took 7-53 to give the Black Caps the upper hand on Friday, looked to target Jadeja but misread a looped delivery from the left-arm spinner and was caught in the deep for four.
Former skipper Tim Southee followed him back into the dugout almost immediately, edging spinner Ashwin to Rohit, who showed quick reflexes to pull off a superb catch at slip and draw loud cheers from the crowd.
Washington took a fine running catch in the deep as Ajaz Patel fell for one to Jadeja while William O'Rourke was run out by the bowler for a duck, leaving Phillips stranded on a well-made 48 not out.
