Electing to bat at the M Chinnaswamy Stadium, the visitors rode on a strokeful 45 by captain and opener Suzie Bates to post 256 all out in 50 overs. Katie Perkins also contributed with a well-made 45 in the middle-order.
Off-spinners Preeti Bose, Sushree Pradhan and leg-spinner Daevika Vaidya bagged three wickets apiece.
In reply, India's chase never really got off after the openers departed early and even a valiant 42 by Priya Punia could not save the hosts from crashing to 159 in 50 overs.
The Mithali Raj-led India begin the five-match ODI series on June 28 followed by three T20 matches.
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Brief Scores:
New Zealand Women 256 all out in 50 overs (Suzie Bates 45, Katie Perkins 45, Amy Satterthwaite 37; Preeti Bose (3-32), Sushree Pradhan (3-52), Daevika Vaidya (3-64)
India A 159 all out in 50 overs (Priya Punia 42, Devika Vaidya 37; Leigh Kasperek (2-22, Morna Nielsen 3-32).