Even hunting a modest 107 on the fifth day against a world-class attack could be nervy, and New Zealand did that after some initial scares.
Will Young (48 not out) and Rachin Ravindra (39 not out) fuelled their chase with a 75-run stand for the third wicket, handholding their side a 1-0 lead in the three-match series.
However, the Indians will not be an entirely despondent lot despite the defeat as they showed admirable spunk to claw back from the depths of getting bowled out for 46 in the first innings.
They will need to build on it and pretty quickly too as the second Test at Pune starts on October 24.
The Rohit Sharma-marshalled side will also have to think deeply about retaining Sarfaraz Khan, who made a 150 in the second dig, as Shubman Gill is poised to return after recovering from a stiff neck.
The other point they will moot long is whether to go back to the three-pacer strategy or continue three spinners, a move which backfired here spectacularly, in Pune.
New Zealand victory did not come without its share of drama once the day’s play started at 10.15am, a wet outfield pushing back the proceedings by an hour.
Bumrah (2/29), operating from the dressing room end, found appreciable movement and Tom Latham fell in the first over of the day itself for his overnight naught.
Latham was behind the ball to cover the in-dipper but it swung back further to thud on to his pads as umpire Michael Gough raised his finger after vociferous appeal from the bowler and the crowd.
The New Zealand captain reviewed the decision more in hope than in conviction and the DRS confirmed his worst fears as well, and he had to walk back.
India might just have felt the absence of a third pacer as both Bumrah and Siraj found movement and carry to trouble the Kiwi batters under a largely overcast skies.
Kuldeep Yadav, who gave away 26 runs in three overs, had replaced Akash Deep in the eleven for this Test after India went with a three-pronged pace attack against Bangladesh recently.
Devon Conway, the other overnight batter, was shaky throughout his stay and would consider himself fortunate to have found a last-minute edge on a Bumrah skidder that otherwise would have trapped him plumb in front.
But as luck would have it, the ball beat the gully fielder and raced to the fence.
However, the left-hander eventually reached the road’s end when Bumrah, operating from around the stumps, caught him right in front of the wicket with another one that skidded and swung back into him.
The on-field umpire did not relent but the DRS upheld India’s appeal to send Conway (17) back.
New Zealand were 35 for two at that point, and one would say the match in balance as a couple of more strikes could have left the cat among the pigeons.
But Young and Ravindra, the first-innings centurion, found some solidity to resist the Indian charge.
Once the sun came out for a while, the ball-movement was much more predictable and the Kiwi batters used favourable conditions to rack in a few boundaries to ease the pressure.
Ravindra Jadeja, who started with a no-ball, too did not make much of an impression, conceding 14 runs in his first two overs.
There was not much on the Chinnaswamy pitch for him to exploit either as the 22-yard track did not disintegrate on the final day, courtesy rain and cooler climes here.
With the margin getting reduced alongside each run, the New Zealand batters became more daring and brought out their shots from the shelf, such as a clean hoist over mid-wicket for a six off left-arm wrist spinner Kuldeep.
The defining moment came when Will Young turned Jadeja for two to collect the winning runs as Kiwis dressing room turned into a hub of celebration.
