The victory gave India six points from two matches, making them the only unbeaten team in the pool following England's surprise 4-1 win over Olympic champions Germany earlier in the day.
New Zealand took the initial lead in the third minute when India conceded a self-goal, which has been introduced into world level hockey after the Olympic Games.
Rupinderpal Singh failed to cleanly stop Sardar Singh's back-pass in front of the goal and the ball trickled over the goal-line to concede India's first self-goal in international hockey.
New Zealand defence also wilted under pressure to give India the equaliser through a self-goal.
Akashdeep Singh dived for a deflection on Sardar long through ball, which went into the goal off a defender to give India the equaliser in the 10th minute.
A fine field goal by Gurwinder Singh Chandi (14th) and a penalty corner conversion by V R Raghunath (25th) gave India a 3-1 lead at the interval before New Zealand came back through a flash strike by Nicholas Wilson two minutes into the second half.
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Mounting pressure through repeated raids, India put the game out of New Zealand's reach when Danish Mujtaba capitalised on a rebound from the goalkeeper on a pressing move in the 65th minute.
This was India's second win in successive days, following the 3-1 win over England in their opening match yesterday.