Series schedule; Photos; Match Scorecard
Spin wizard Ravichandran Ashwin blew away the lower order with another superb effort of 6 for 55 as England were bundled out for 195 in 55.3 overs with just 8 overs being required on the final day.
This is the first time in India that a visiting team has lost a Test match after scoring 400 runs in their first innings. Ashwin got his 7th 10-wicket haul in Test cricket to finish with match-figures of 12 for 167 and now only has chief coach Anil Kumble's milestone of eight 10-fors in front of him.
(Twitterati hail Virat Kohli and Company's historic win at Wankhede)
This is also the 5th successive series win under Virat Kohli having started the juggernaut last year in Sri Lanka (away) followed by South Africa (home), West Indies (away), New Zealand (home) and now England.
The series win also meant that India regained the Anthony de Mello Trophy having lost it to Alastair Cook's men in 2012. The next Test in Chennai starting December 16-20 has now been rendered inconsequential.
There was no resistance from England in the morning session as Ashwin took four wickets in four overs to complete the formalities.
Jonny Bairstow (51) was out to a carrom ball, Chris Woakes (0) was dismissed by an off-break while Adil Rashid's flick to deep mid-wicket completed his 24th five-wicket haul in Tests.
The moment Anderson flicked one to Umesh Yadav, it was all over in a flash as Ashwin and centurion Murali Vijay picked up a stump each as souvenirs.
Acknowledging the capacity Wankhede crowd which has provided vociferous support, the Indian team led by their charismatic skipper Kohli took a lap of honour as the entire stadium gave them a standing ovation.
It was a Test match where India literally dominated the proceedings save the first day.
Skipper Kohli again led from the front with an inspirational show that saw him pile up 640 runs in four Test matches with an astounding average of 128.
His 'go-to' man Ashwin also intimidated the visitors with 27 wickets in the series. Not to forget 239 runs with the bat. Rookie Jayant Yadav has been the find of the series with 221 runs and 9 wickets so far.
The supporting cast of Cheteshwar Pujara (385 runs), Murali Vijay (328 runs) and Ravindra Jadeja (16 wickets) have also played their parts admirably.