Andrew Hayward was the key man in the Black Sticks' 3-1 success, scoring one penalty corner, creating another from a set-piece and also hitting the post on one routine.
New Zealand's first points put them back in touch with the upper reaches of the group, although they remain three behind leaders the Netherlands in Pool B.
India had got off to the perfect start when Sandeep Singh flicked in a high penalty corner in the first couple of minutes.
But New Zealand hit back and Hayward first hit a post before flicking home the equaliser and when another goalbound set-piece was stopped on the line by the body of Birendra Lakra, Phil Burrows stepped up to convert from the penalty spot.
They extended their lead when Shea McAleese's run to the byline allowed him to cut the ball back for Nick Wilson to sweep home.
India produced a spirited second-half performance in their opener against the Netherlands, coming back from two goals down only to eventually lose 3-2, and they certainly stepped things up after the break.
But the closest they came to reducing the deficit, despite a succession of penalty corners, was when VR Raghunath hit the post from a 65th-minute set-piece.