Ravichandran Ashwin claimed six wickets to help dismiss New Zealand for 299 and put India in pole position with a 258-run first innings lead in the third and final Test on Monday.
India, who did not enforce the follow-on, were 18 for no loss in their second innings at stumps on day three, with Murali Vijay (11) and Cheteshwar Pujara (1) stretching the lead to 276 in their quest to complete a series whitewash at Indore.
Opener Gautam Gambhir retired hurt on six after aggravating a shoulder injury, which he first suffered while fielding, as he dived into his crease to avoid a run-out.
Earlier off-spinner Ashwin ensured that India continue their domination of the series at their newest Test venue, Indore's Holkar Stadium, after recording his 20th five-wicket haul to destroy the New Zealand batting.
Opener Martin Guptill, who struck form with a gritty 72, and James Neesham (71) put up the main resistance against an inspired Indian attack.
The Black Caps, who began the day on 28 without loss, had made a strong start in response to India's commanding first innings score of 557 for five declared, but then lost five wickets for just 30 runs.
After Tom Latham fell just before lunch for 53, caught and bowled by Ashwin, India turned the screws on the visitors by taking a further five wickets in the afternoon session.
Guptill counter-attacked the Indian bowlers with 10 fours and two sixes during his 144-ball stay but was unlucky to be run out by Ashwin while backing up.
Ashwin's other victims included New Zealand skipper Kane Williamson, who was bowled for eight early on after dragging a turning delivery onto his stumps. It was the third time in a row he had been dismissed by Ashwin.
Neesham and B.J. Watling put on 53 for the sixth wicket to raise hopes of a revival, but left-arm spinner Ravindra Jadeja broke the stand by bowling Watling for 23 after the wicketkeeper-batsman had struck four boundaries.
Neesham carried on the good work after tea to register his fourth Test fifty in 10 games but ran out of steam after being trapped lbw by Ashwin, who soon wiped out the tail.
Indian skipper Virat Kohli had played a vital role Sunday with a career-best 211, his second double-century in Tests.
Kohli's record 365-run fourth-wicket stand with Ajinkya Rahane (188) was the highlight of India's first innings after the hosts elected to bat first.
India, who took an unassailable 2-0 lead in Kolkata, are looking to complete their second home series whitewash against New Zealand in succession.