Put in to bat, Finn Allen gave New Zealand a quick start with 35 off 23 balls. He struck four fours and two sixes, putting on 43 off 26 balls with Conway.
Washington Sundar (2-22) struck twice to remove Allen and Mark Chapman, the latter for a duck via a stunning return catch.
Conway, though, scored a half-century off 31 balls, including seven fours and a six to steer New Zealand to 100 in the 13th over.
Conway fell on 52 in the 18th over to Arshdeep Singh, but Mitchell pressed on.
His 26-ball half-century powered the total past 170. Mitchell hit three fours and five sixes as Singh gave away 27 runs in the final over.
In reply, India got off to a poor start due to the Kiwi spinners squeezing the scoreboard.
Bracewell bowled Ishan Kishan (four) and Santner got rid of the in-form Shubman Gill (seven). Rahul Tripathi was caught behind for a duck and India were down to 15-3 in the fourth over.
Suryakumar Yadav scored 47 off 34 balls and added 68 runs for the fourth wicket with Hardik Pandya, who scored 21.
But the duo were undone when the spinners returned.
Yadav holed out off Ish Sodhi, and Pandya fell to Bracewell. Santner had Deepak Hooda stumped on 10 and the India innings was in tatters at 111-6 in the 16th over.
Sundar’s 50 included five fours and three sixes but his maiden T20 half-century off 25 balls could only reduce New Zealand’s winning margin.
The second of three T20s is on Monday in Lucknow.
As it happened: all the action from the first T20 between the Black Caps and India in Ranchi.
