Virat Kohli (L) with teammate Sanju Samson (R) celebrate their win during the fourth Twenty20 match at Sky Stadium in Wellington on Friday. AFP
New Zealand, batting first in the decider, made 13 with Tim Seifert dropped twice before he was eventually dismissed.
In reply, Indian captain Virat Kohli hit the winning runs with a ball to spare.
The third match also ended in a Super Over with Rohit Sharma hitting sixes off the last two balls to get India home.
"What's happened in the last two games is unbelievable," Kohli said.
"It feels good when you are out of the game and then somehow find a way to come back and that shows the character of the team."
The win puts India 4-0 up in the five match series with New Zealand stand-in captain Tim Southee not happy that his side could not wrap the game up in the 20 overs.
"It's very tough, especially in the position we got ourselves into and then to give them a chance at the end, they're going to grab it with both hands," he said.
New Zealand, chasing India's 165 for eight, went into their last over only needing seven runs to win and with seven wickets in hand.
However, they were restricted to six runs and lost four wickets to finish 165 for seven and set up the Super Over.
New Zealand had already suffered an earlier setback with talismanic captain Kane Williamson a late scratching having not fully recovered from a shoulder injury suffered while fielding in game three.
It was left to lusty hitting by Colin Munro and Seifert to provide the backbone of their innings with Munro making 64 and Seifert out in the final over for 57.
India, sent into bat first, made 165 for eight on a flat track at Wellington stadium with the innings anchored by an unbeaten 50 from Manish Pandey and his partnerships with Thakur and Navdeep Saini.
India were six for 88 in the 12th over before Pandey and Thakur arrested the slide in a 43-run stand with Thakur contributing 20.
Saini, who was not out 11 in his first appearance on tour, put on 22 with Pandey off the last 13 deliveries.
In a slow start to their reply, New Zealand were 23 for one after five overs.
But in the sixth over, when Thakur wound back the pace to under 140 kilometres per hour (87mph), Munro found his timing with a six and two fours to get the scoreboard moving.
In partnership with Seifert they put on 72 off 44 deliveries before Munro was run out in a smart piece of relay fielding involving Thakur and Kohli who threw down the stumps.
Sharma put on a key 137-run second-wicket stand with skipper Virat Kohli, who made 89, as India chased down their target of 287 in 47.3 overs. Shreyas Iyer was unbeaten on 44.
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Prithvi hit nine boundaries and one six during his stint at the crease. He was well supported by Shikhar Dhawan (33).
Both Kolkata Knight Riders (KKR) and Sunrisers Hyderabad (SRH) will look to put their stuttering campaign back on track after losses in their opening matches in the Indian Premier League (IPL).