India crush England by an innings to seal Test series 4-1
England's James Anderson reached 700 Test wickets early in the day to be just the third bowler to achieve the feat, but the tourists were never in the game.
Off-spinner Ashwin returned figures of 5-77 to help bowl out England for 195 inside three days at the picturesque Dharamsala stadium, overlooked by snowcapped Himalayan mountains, after India posted a mammoth 477.
He rocked England's top- and middle-order after the tourists began their innings 259 runs behind and lost five wickets for 103 runs by lunch.
After the match, Ashwin said he was "very happy" with his performance.
"Win the Test and take wickets, what more can a bowler ask for?"
Jonny Bairstow, also in his 100th Test, attempted to take on the spinners and hit Ashwin for three sixes but finally fell lbw to Kuldeep Yadav after his 31-ball 39.
At the stroke of lunch Ashwin bowled skipper Ben Stokes for two, taking down the star all-rounder for the 13th time in Tests.
Joe Root resisted with his 84 and was the last man to go. He was dismissed by Yadav as India celebrated and the players shook hands.
Ashwin finished with nine wickets in the match and his 36th five-wicket haul in a career which began in 2011.
Skipper Rohit Sharma did not take the field due to a "stiff back", with fast bowler deputy Jasprit Bumrah in charge and taking two wickets of his own.
Earlier, Anderson got Yadav caught behind for 30 to become the first paceman and third bowler overall to the 700 mark, after spinners Muttiah Muralitharan of Sri Lanka (800 wickets) and late Australian great Shane Warne (708).
The 41-year-old held the ball aloft to the crowd as teammates gathered around him and England fans stood to cheer.
It ended Yadav's stubborn 49-run ninth-wicket overnight stand with Bumrah.
Spinner Shoaib Bashir soon wrapped up the innings in the fifth over of the day when he got Bumrah stumped for 20, completing the 20-year-old's second five-wicket haul in his debut series.
Rohit (103) and Shubman Gill (110) set up the huge victory on the second day with a 171-run second-wicket stand to put the England bowlers on the back foot.
Rookie batsman Sarfaraz Khan (56) and debutant Devdutt Padikkal (65) also made useful contributions in India's sole innings in response to England's 218.
India opener Yashasvi Jaiswal scored 57 and remained the leading batsman in the series with 712 runs, including double centuries in matches two and three.
Yadav made his left-arm wrist spin count with his own five-wicket haul to bundle England out on day one after the visitors elected to bat first.
England won the opener by 28 runs in Hyderabad with their attacking "Bazball" style of play, which came under fire by the critics in the next three losses, after they suffered regular batting flops.