New Zealand were all out for 62 in their first innings in reply to India's 325, with the tourists trailing by 263 runs on the second day of the final test at the Wankhede Stadium on Saturday.
India off-spinner Ravichandran Ashwin picked up four wickets for eight runs while his fast bowling colleague Mohammed Siraj chipped in with 3-19.
Mayank Agarwal was the top-scorer for the hosts with a knock of 150 while Ajaz Patel picked up all wickets for New Zealand to post figures of 10-119.
Source: Reuters