Rachin Ravindra and Will Young remained calm under pressure after the loss of two early wickets to get the job done, earning New Zealand only their third win on Indian soil in 38 attempts going back to 1955.
New Zealand secured an eight-wicket win for their first Test victory in India since 1988 as the Black Caps chased down 107 and humbled the home side early on the final day of the rain-interrupted series opener on Sunday.
After dismissing India for their worst home total of 46 and making 402 in reply, New Zealand bowled out Rohit Sharma's side for 462 in the second innings on Saturday to lay the platform for a 1-0 lead in the three-match series.
Rachin Ravindra and Will Young remained calm under pressure after the loss of two early wickets to get the job done, earning New Zealand only their third win on Indian soil in 38 attempts going back to 1955.
New Zealand got off to a wobbly start when play began after a rain delay, as new permanent skipper Tom Latham was trapped lbw by Jasprit Bumrah on the second ball of the day for a duck with the tourists yet to score.
Bumrah and fellow pace bowler Mohammed Siraj made life hell for the New Zealand batsmen early in the day, as India looked to do what no team have done in Test history and win a match after conceding a first-innings lead of more than 350 runs.
Conway endured a couple of painful body blows, balls that whizzed past the blade and unfriendly glares from the bowlers amid jeers from partisan fans at the M Chinnaswamy Stadium before falling lbw to Bumrah for 17.
The wicket appeared to turn placid after that dismissal as New Zealand cruised to a famous victory.
