Opting to bat, the hosts had the worst possible start as Mohammed Shami struck early sending back both the openers — Martin Guptill and Colin Munro, cheaply.
Kane Williamson and Ross Taylor then tried to rescue their side from the early damage, taking New Zealand past the 50-run mark in 13.3 overs.
However, Taylor's stay was cut short by Chahal in the 15th over with the hosts at 52/3. With the addition of just 24 runs in the Kiwi scorecard, Chahal struck again to dismiss incoming batsman Tom Latham.
Jadhav and Shami then joined the party as they sent back Henry Nicholls and Mitchell Santner, leaving the hosts reeling at 133/6. Williamson, however, continued to show resistance and kept one end safe, but lacked support from the other end.
While trying to clear the fence in the 34th over off a Kuldeep delivery, the Kiwi skipper misread the ball and offered a simple catch to Vijay Shankar at long-on.
Kuldeep then put the final nail in the coffin, picking the tailenders — Doug Bracewell, Lockie Ferguson and Trent Boult in quick succession to wrap up the host in just 38 overs. Mohammed Shami, Kuldeep Yadav and Yuzvendra Chahal's combined figures read 26 overs 3 maidens 9 wickets for 101 runs.
India got off to a cautious start in the 158 run start.. Rohit and Shikhar stictched a 41 run stand before the right hander pocked a ball outside the off stump to be caught in the slips for 11 runs.
Captain Virat joined Shikhar and the duo kept finding holes in the kiwi field to stitch a 91 stand for the 2nd wicket.
Virat missed his half century by 5 runs to depart for 45 runs. Shikhar and Ambyati Rayadu took India home under the duckworth lewis method with 85 deiveries and 8 wickets to spare.
India crossed the line and the action now shifts to the 2nd ODI on Saturday. Mohammed Shami bagged the man of the match award.