England were bowled out for 195 in the morning session of the fifth day, after resuming on the overnight 182/6 in their second innings, and still trailing by 49 runs.
It was the hosts' first series win in four attempts against England with their previous triumph coming in 2008.
This is only the third time that a team has suffered an innings defeat after scoring 400 runs or more in the first innings of a Test. England losing to Australia at The Oval in 1930 and Sri Lanka going down to England in Cardiff in 2011 are the only previous instances.
Jonny Bairstow (51) was the first to get out in the morning, followed by Ben Stokes (18), Adil Rashid (2), and James Anderson (2).
Star off-spinner Ravichandran Ashwin dismantled England, picking up 6/55 in the second innings to take a total of 12 wickets in the match.
Left-arm spinner Ravindra Jadeja returned figures of 2/63 while pacer Bhuvneshwah Kumar and rookie spinner Jayant Yadav claimed a wicket each.
Ashwin's match haul of 12/167 is the best by any Indian bowler at the Wankhede Stadium. It is also the second best by any bowler at this venue behind England legend Ian Botham's 13/106 in 1980.
The Tamil Nadu spinner now has 24 hauls of five wickets or more in Test matches. He has surpassed the legendary Kapil Dev to take the third place in India's all-time list. Only leg spin great and current Indian coach Kumble and former off-spinner Harbhajan Singh have more with 35 and 25 respectively.
Ashwin's record of seven 10-wicket hauls in Test matches is just one short of the Indian record of eight by Kumble.
India captain Virat Kohli, who scored a double century during India's first innings, was adjudged the Man of the Match.
Kohli scored 235 runs, his third double century of the year.
With in-form rookie Jayant Yadav scoring 104 at the other end, the duo put together a partnership of 241 runs to help the hosts amass a formidable first innings score of 631 runs on the fourth day.
India have now won five Test series in a row. During this period, they have won at home against South Africa, New Zealand and England, and away in Sri Lanka and the West Indies.
The Indian team had earlier won five consecutive Test series between 2008 and 2010 -- at home against Australia, England and Sri Lanka, and away in New Zealand and Bangladesh.
This is the 17th consecutive Test in which India have remained unbeaten. They have won 13 of those and drawn four.
This equals India's longest ever unbeaten run -- they also went 17 Tests without a defeat between September 1985 and March 1987. On that occasion, they won four Tests and drew 12 while one was tied.
India coach Anil Kumble praised his wards and asserted that the current batch of players are among the best to represent the country over the years.
"You cannot really compare with the teams of the past. Those were different eras and different teams. But this team certainly is the number one team in the world today and has the potential to be the best ever Test team in terms of results," Kumble said at the end of the match.
"They have done well over the last couple of years. The team is exceptional in terms of the intensity that they have showed on the field and in terms of situational awareness. They are coming out of difficult situations in this series and also in the series against New Zealand.
"Everyone has contributed to the team's success. That is the beauty about this team. I do not really like to compare but this team is certainly special. I am privileged to be a part of this set up," he added.
The Indians did not have to wait long for the first wicket of the day as Ashwin trapped Jonny Bairstow leg before.
Bairstow, who was the second highest scorer in England's second innings with 51 runs, called for a review, but the third umpire backed the original decision.
Chris Woakes went back before opening his account. The right-hander went for a drive, but Ashwin managed to find the gap between his bat and pad and the ball crashed into the stumps.
Ashwin then cleaned up the wickets of Adil Rashid and James Anderson to clinch a well-deserved victory for India.