Lalit Upadhyay (7th minute), Harjeet Singh (32nd) and Rupinder Pal Singh (36th) scored for India while New Zealand's goals came from sticks of Daniel Harris (23rd) and Kane Russell (37th).
The home team were dominant early on and were quick to make potential circle penetrations but the Indian defence stood tall.
India made a breakthrough soon when skipper Manpreet Singh found Vivek Sagar Prasad swiftly moving towards the top of the circle. But Vivek's reverse hit rebounded off the New Zealand keeper and found Lalit who scored past Devon Manchester to give India a 1-0 lead.
One such circle penetration won New Zealand their first penalty corner of the match but Russell's drag flick was well saved by Sreejesh.
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An error by an Indian defender saw New Zealand equalise in the following minutes when Harris scored from a rebound.
India came back with a fresh approach after the change of ends and striker Mandeep Singh was clever to earn their first penalty corner of the match in the 32nd minute which was successfully converted by Harjeet.
A minute later, New Zealand bagged a penalty corner which was successfully executed by Russell, who kept it low to the left pocket.
Though New Zealand won another penalty corner in the following minutes, Russell shot wide.
The last quarter saw New Zealand make desperate attempts to equalise but their efforts were constantly kept at bay by the Indian defence.
India will next take on Belgium in their second match.