India's Ravichandran Ashwin (R) celebrates after the wicket of New Zealand's Jeetan Patel.
PHOTO: REUTERS
Ashwin with career-best match figures of 13-140 helped India skittle out the visitors, who were chasing a daunting 475-run target, for 153 in under two sessions of play at Indore.
Ashwin, the highest wicket-taker in the three Tests with 27 scalps, was named both man of the match and player of the series.
India, who climbed to the top of the world Test rankings after their series-clinching win in Kolkata, remain in number one position ahead of Pakistan.
New Zealand, whitewashed in India for the second successive time after their 2-0 loss in 2012, suffered an early blow when Umesh Yadav trapped opener Tom Latham lbw for six.
The visitors took tea on 38 for one but lost nine more wickets in the final session of play.
India take charge of Indore Test after Ashwin's heroics
The spinner, who registered his 21st five-wicket haul in Tests, took charge in the evening session to remove skipper Kane Williamson for 27.
It was the fourth time in a row that the Black Caps' star batsman, who missed the second Test due to a viral infection, had been dismissed by Ashwin.
Ross Taylor showed some aggressive intent with 32 off 25 balls including five fours and a six, but did not last long before he was bowled by another Ashwin turner.
Left-arm spinner Ravindra Jadeja soon joined forces with Ashwin to dash New Zealnd's hopes of surviving the day after getting the all-important wickets of Martin Guptill and James Neesham.
Earlier in the day, a century by Cheteshwar Pujara put the hosts on course to set New Zealand a daunting victory target at India's newest Test venue, Indore's Holkar Stadium.
Pujara struck an unbeaten 101 as India, who started the day on 18 without loss, declared their second innings on 216 for three in the afternoon session.
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Pujara, who recorded his eight Test hundred, put on 76 for the second wicket with recalled opener Gautam Gambhir (50).
Gambhir had retired hurt on Monday after aggravating his shoulder injury while diving to save himself from being run out.
India had already gained the upper hand after bowling out New Zealand for 299 in response to their massive first innings score of 557 for five declared.
Skipper Virat Kohli's second Test double-century paved the way for India's dominance as he registered his career-best score of 211.
The star batsman put on a record 365-run fourth-wicket partnership with Ajinkya Rahane (188) to keep the New Zealand bowlers on the field for close to six sessions.
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