The very next delivery a Rohit Sharma pull shot picked out Santner on the fence as he took a brilliant low-diving catch.
India made their way through to 67 in their allotment, putting the pressure on the Black Caps.
New Zealand's batsmen struggled to make much headway. Captain Kane Williamson was run out by a direct hit from Hardik Pandya running to the non-striker's end.
Glenn Phillips briefly threatened in getting to 11 before holing out to deep mid wicket, while Colin de Grandhomme, after one flat six which whistled over the boundary, finished on 17 off 10 balls.
New Zealand needed 32 off the last three overs and 19 off the last bowled by Pandya.
De Grandhomme's second six of the innings, lifting Pandya over mid wicket off the third ball, left New Zealand needing 12 off the last three, but the bowler held his nerve.
"It was quite hard to know what a good first innings score was on that surface but credit to the ground staff for getting the game ready," Williamson said.
"It was a tricky surface and runs on the board on that surface were handy.
"Credit to India, they deserved to win the series, although it came down to the last couple of deliveries. It was just a shame we didn't get across the line in this decider."
Williamson liked the fight his team had shown but pointed out there were good lessons to be learned by his players.
"You have to be at the top of your game to win a series over here. One-off games, yes, that's great, but you do need to get better throughout.
"That's why [India are] possibly the best team in the world because they challenge you in all areas and put you under a lot of pressure."