New Zealand have won their first Test on Indian soil since 1988 after the home side collapsed in the second innings.
After a rain-affected day four, the Black Caps cruised towards victory on Sunday, losing just two wickets as Rachin Ravindra and Will Young finished unbeaten.
India lost seven wickets for just 54 runs in its second innings, collapsing to 462 all out in 99.3 overs, just days after being rolled for an embarrassing 46 in their first dig.
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Rishabh Pant (99) and Sarfaraz Khan (150) both helped the hosts back into the contest, but once they were dismissed it was chaos for India, who lost six wickets for 29 runs.
Overall, Khan hit 18 fours and three sixes, while Pant smacked nine fours and five sixes.
Tim Southee had Khan caught in the 85th over, but the big moment came when O’Rourke bowled Pant in the 89th.
It ushered in India’s collapse, with the lower-middle order unable to resist the new ball.
O’Rourke had Lokesh Rahul caught behind for 12, while Ravindra Jadeja was out for five.
Henry trapped Ravichandran Ashwin lbw for 15 and then removed the tailenders in the space of six deliveries. India lost its last six wickets for 29 runs across 68 deliveries.
Rain prevented any further play after just four deliveries in the Kiwi innings. Jasprit Bumrah had a loud lbw shout turned down against Tom Latham as India lost a review.
Requiring just 107 runs to win on day five, New Zealand got off to a shaky start when Tom Latham was out for a duck, but Ravindra (39 not out) and Young (48 not out) steadied the ship and gave their side a 1-0 lead in the three-game series.
The second match in the three-Test series will be played in Pune starting next Thursday AEDT and the final one in Mumbai from November 1.