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Virat Kohli struck 95 off 105 balls and shared 78 runs with Ravindra Jadeja (39 not out) for the sixth wicket to chase down the 274-run target in 48 overs.
Captain Rohit Sharma contributed 46 off 40 balls at the top of batting order.
Lockie Ferguson was the most successful New Zealand bowler with figures of 2 for 63. Earlier, pacer Mohammed Shami grabbed 5/54 in his comeback game to help India restrict New Zealand to 273.
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New Zealand lost openers Devon Conway (0) and Will Young (17) cheaply, but thereafter Mitchell and Rachin Ravindra (75) shared a 159-run partnership to revive their innings.
Brief Scores:
New Zealand 273 in 50 overs (Daryl Mitchell 130, Rachin Ravindra 75; Mohammed Shami 5/54).
India: 274 for 6 in 48 overs (Virat Kohli 95, Rohit Sharma 46; Lockie Ferguson 2/63).