The last time India were blanked at home was in 2000, in a two-match series against South Africa.Â
Rohit Sharma's side will be feeling the heat ahead of a challenging five-match series against Australia.
Rishabh Pant was the lone Indian batsman to show resistance, making a sublime 64 after the hosts were reduced to 5-29 on a turning Wankhede Stadium track.
Ajaz Patel claimed 6-57, his second five-wicket haul in the match, to again skittle the hosts.
Sharma threw the first punch by stepping out of his crease to hit Matt Henry for a four in the opening over, but the skipper's disappointing recent run of form continued when he fell for 11 after a rash shot against the same bowler.
Patel made it two wickets in two overs when Shubman Gill, who had scored a splendid 90 in the first innings, left a ball that crashed into the stumps and departed for just one run.
Virat Kohli did not last long, edging Patel to slip on one to leave India in real trouble at 3-18 .
The crowd fell silent again when Yashasvi Jaiswal was trapped lbw for five by Glenn Phillips and Sarfaraz Khan hit a full toss from Patel straight to Rachin Ravindra in the deep on one.
Ravindra Jadeja steadied the ship alongside Pant in a 42-run stand, but a stunning catch by Will Young meant India were on the ropes at 6-71.
Patel dismissed Pant following a New Zealand review after lunch, although the batsman appeared to suggest he had not made contact with the ball before it was caught.
The runs dried up after that and India collapsed in a heap.
New Zealand had earlier resumed their second innings on 9-171, but India needed only 14 balls to bowl the Black Caps out. Jadeja had Patel caught in the deep to end with the fine figures of 5-55 after also bagging five in the first innings.
The tourists won the opening match in Bengaluru by eight wickets for their first Test victory in India in 36 years, then wrapped up the series with a 113-run win in Pune.
New Zealand's maiden series triumph in India going back to 1955 also snapped the hosts' home streak of 18 straight series triumphs since a 2-1 loss to England in 2012.
