The oversaturated cricket calendar has forced several high-profile players to miss matches throughout 2021.
Australian powerhouses David Warner and Pat Cummins skipped winter tours of the West Indies and Bangladesh ahead of the T20 World Cup, while England was forced to adopt a rotation policy for its Test side, which will play 16 Test matches in 2021.
Dozens of players also missed the second leg of the Indian Premier League due to bubble fatigue.
Fans and cricket pundits were left baffled by the timing of the series, with Australian journalist Daniel Cherny saying ahead of the game: "This is just so stupid."
Thursday's match marked the first for new Indian captain Rohit Sharma and coach Rahul Dravid, who have replaced Kohli and Ravi Shastri respectively.
India gave Sharma a winning start as captain, cruising towards the 165-run target as Suryakumar Yadav made 62.
From needing 23 from the final four overs with eight wickets in hand, India stuttered badly to leave them still requiring 10 off the last over, bowled by part-time seamer Daryl Mitchell.
But Rishabh Pant struck the winning boundary over mid-off with two balls to spare to put India 1-0 ahead in the three-match series.
"Towards the end we saw it wasn't easy. Was a great learning for the guys because those guys haven't batted in that situation before for India," Sharma said.
Yadav, who was given the player-of-the-match award, struck six fours and three sixes in his 40-ball innings before he was clean bowled by Trent Boult, who earlier removed Rohit, in the 16th over.
New Zealand dragged themselves back into the contest in the closing overs, but stand-in skipper Tim Southee turned to Mitchell instead of leg-spinner Todd Astle in the 20th over and Pant got India over the line.
"We played our best cricket and took it deep," Southee said.
Earlier, half-centuries by Martin Guptill and Mark Chapman propelled the visitors to a score of 164/6.
The teams will meet in the second T20I on Friday in Ranchi.
