Jayant Yadav struck in the seventh over of the day to break the resisting 33-run stand between Ravindra and Nicholls.
Jayant then backed it up with a two-wicket over as India closed in on their series win.
New Zealand's innings on Day 4 lasted all of 11.3 overs as India cruised to a 372-run win - their biggest ever - to bag the series 1-0. Jayant and Ashwin returned four-wicket hauls.