Hugo Inglis's clinical finish low and hard into the bottom right corner gave the Black Sticks the lead after seven minutes, Stephen Jenness doubling the margin two minutes out from the first break.
The New Zealanders looked set to maintain their 2-0 lead into half-time, but India earned a penalty corner - and Kiwi skipper Arun Panchia a yellow card - with less than a minute remaining.
From there, a penalty stroke was awarded, which Harmanpreet Singh duly converted for his fifth goal of the Games, and India went into the break only a goal down.
Marcus Child slammed home for New Zealand's third four minutes out from three-quarter time, the Black Sticks taking a 3-1 lead into the break on the back out some outstanding work from keeper Richard Joyce.
India piled the pressure on in the closing minutes, forcing four penalty corners in rapid succession, with Harmanpreet slamming home from the fourth to set up a grandstand finish.
- AAP