Ravichandran Ashwin wrecks England in Dharamsala as India win series 4-1
The hosts held an unassailable 3-1 lead heading into the match and were on the ascendancy since taking a first innings lead of 259.
Ravichandran Ashwin (5-77) wrecked England's top order and India eventually shot out the tourists for 195 with only Joe Root (84) offering some resistance with the bat.
"To win a test series, a lot of things have to fall into place and go right and our players did that, and that's why we are standing here with this series result," India captain Rohit Sharma said.
India were without several frontline players and fielded five debutants in the series.
Rohit was pleased with how the likes of Dhruv Jurel and Sarfaraz Khan responded to the challenge.
"They responded very well to pressure throughout the series and there were a lot of times where we came back from behind during the series."
Resuming on 473-8, India could add only four runs before losing their last two wickets when play restarted on day three.
England warhorse James Anderson became the first fast bowler to claim 700 test wickets, when he dismissed Kuldeep (30) caught behind.
India harnessed Ashwin with Jasprit Bumrah for new ball duties and the off-spinner bowled Ben Duckett (two) in his first over.
Ashwin struck again in his third over, dismissing Zak Crawley for a duck.
Ollie Pope made a breezy 19 before attempting a sweep against Ashwin, and Yashasvi Jaiswal took a running catch to dismiss the England vice-captain.
Jonny Bairstow smacked Ashwin for three sixes in an enthralling duel between two fierce competitors both playing their 100th tests.
Kuldeep Yadav, replacing Ashwin in the attack, ended Bairstow's entertaining knock of 39, trapping him lbw.
Ashwin returned to disturb Stokes' stumps with the final delivery before the lunch break after which England's defeat was only a matter of time.
Root waged a lone battle but did not get much support from the other end and was the last man out.
"We are man enough and big enough to accept that we have been outplayed by the better team since the first test," Stokes said afterwards.
"We are going to take the positives from this series with the amount of cricket that we have got coming up and I'm really looking forward to drive this team even further forward."
Kuldeep was adjudged player of the match primarily for his five-wicket haul in the first innings.
India opener Jaiswal won the player of the series for his aggregate of 712 runs, which included two double hundreds, from nine innings.
This was India's 17th consecutive test series win at home, where they have not lost a test series since an Alastair Cook-led England bested them in 2012.