The seven-wicket triumph was set up by skipper Rohit Sharma (50, 29b) and Shikhar Dhawan (30, 31b) with a 79-run stand after Krunal Pandya claimed three wickets to restrict New Zealand to 158 for eight.
Rohit made a whirlwind fifty off 29 balls. Rishabh Pant finished it off unbeaten on 40 off 28.
MS Dhoni (20*) and Pant (40*) then knocked off the remaining runs easily to lead India home with seven balls remaining.
Earlier, An umpiring error that promises to make headlines in the days to come threatened to overshadow a vastly improved effort in the field from India that had NZ limping to 158/8 in 20 overs.
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Krunal Pandya was the man of the match for his 3/28.
Mahendra Singh Dhoni watched from the 22 yards distance as his heir apparent Rishabh Pant showed spunk in a tricky situation, guiding India to its maiden T20 global victory on New Zealand soil here Friday. For the record, New Zealand have lost four of their last five T20Is at Eden Park. From the nonstriker's end, Williamson walked down to Mitchell - playing his second worldwide match - and had a word with his partner after which the rookie requested a review.
TV replays clearly showed there was an inside edge and a patch on the hotspot could also be detected when the ball beat Mitchell's bat. But, he was still given out by third umpire Shaun Haig. It was dead in front of the stumps, so there was no need to review. He and Bhuvneshwar also bowled 18 dot balls between them.
When he was just about threatening to take the game away, de Grandhomme smacked one straight to covers in skipper Rohit's hands.
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The Black Caps, who thumped India by 80 runs in the series opener in Wellington, posted 158-8 with Colin de Grandhomme (50 off 28 balls) and Ross Taylor (42 off 36) sharing a fifth-wicket stand of 77 and Krunal bagging 3-28, Kane Williamson and Colin Munro his other scalps.
Hardik spilled a diving catch at long-on to allow Scott Kuggeleijm first ball, but Khaleel bowled Mitchell Santner and Tim Southee to end the innings superbly.
Editorial team of CricketCountry.
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