New Zealand resumed their second innings on 93 for four at the start of the fifth and final day in pursuit of an unlikely 434-run victory target, but were bowled out shortly after lunch for 236.
Ashwin, who recorded his 19th five-wicket haul in Tests, and left-arm spinner Ravindra Jadeja shared 16 wickets between them in the match to flatten the New Zealand batting at Kanpur’s Green Park.
The lanky off-spinner got Neil Wagner lbw for nought to end with overall match figures of 10-225 and trigger wild celebrations in the Indian camp.
A 102-run partnership between overnight batsmen Luke Ronchi and Mitchell Santner helped New Zealand put up some resistance in the first hour of play. Ronchi’s fighting 80 was laced with nine fours and a six.
But left-arm spinner Jadeja, who registered a five-wicket haul in the first innings, managed to break their stand when Ronchi mistimed a flatter delivery and was caught at point by Ashwin.
Santner, whose valiant 71 included seven fours and two sixes, was snared by Ashwin shortly after lunch when he fell to a virtually unplayable delivery.
The ball pitched well outside the leg-stump and turned and bounced to take the left-handed Santner by surprise as he edged the ball to point.
Pace spearhead Mohammed Shami also claimed two wickets in the innings, including wicketkeeper-batsman BJ Watling for 18.
Ashwin claimed three wickets on Sunday to reduce New Zealand to 56 for four at one stage, after getting openers Martin Guptill and Tom Latham in quick succession.
Ashwin also had skipper Kane Williamson, who top-scored with 75 in the first innings, dismissed lbw to claim his 200th Test wicket on the fourth day to give India a firm grip.
India declared their second innings on 377 for five at tea on the fourth day with Rohit Sharma and Jadeja putting on a 100-run unbeaten partnership for the sixth wicket.
Cheteshwar Pujara top-scored for the hosts with 78 and his 133-run second-wicket partnership with Murali Vijay (76) was the highlight of India’s second innings.
Ashwin and Jadeja had given India the advantage on the third day after bowling out New Zealand for 262 in response to India’s first-innings 318.