The Black Caps, who started day three on 152 for one, faltered in the second session while responding to India’s first innings score of 318.
Jadeja, who claimed a five-wicket haul, combined forces with Ashwin to derail New Zealand’s reply after getting overnight batsmen Kane Williamson and Tom Latham in the morning session.
The spin twins continued to wreak havoc after lunch as Jadeja, who was denied a hat-trick, wiped off the opposition tail after taking three wickets in the 95th over of the innings.
New Zealand lost five wickets for just seven runs as they nosedived from 255 for five to pack up in 95.5 overs.
The second-wicket partnership between Williamson, who top-scored with 75, and Latham, who contributed 58, remained the highlight of the New Zealand innings.