Ashwin bags six wickets as India hammer Bangladesh in first Test
The tourists, who began day four in an overcast Chennai on 158-4 and chasing 515 for victory, were bowled out for 234 in the first session with skipper Najmul Hossain Shanto scoring 82.
Hometown hero Ashwin struck first to end a stubborn overnight stand by getting Shakib Al Hasan caught at short-leg for 25.
The spinner, who took three wickets on day three, then dismissed Mehidy Hasan Miraz for one to bag his 37th five-wicket haul.
The feat added to his heroics after his 113 guided the hosts to 376 in the first innings.
Shakib put on 48 runs with skipper Najmul after the pair started cautiously.
Left-arm spinner Ravindra Jadeja removed Litton Das for one after the wicketkeeper-batsman edged the ball to skipper Rohit Sharma at first slip.
Jadeja ended Najmul's valiant stand and took three wickets for the innings.
Spin twins Ashwin and Jadeja had played a key batting role in the first innings when their 199-run seventh-wicket stand lifted India from a precarious 144-6 to a challenging total on the first day.
India declared their second innings at 287-4 on day three after centuries from Shubman Gill, who hit an unbeaten 119, and returning Rishabh Pant, who made 109, flattened the opposition.
Gill and the left-handed Pant, who is playing his first Test since a serious car crash in December 2022, put on 167 runs for the fourth wicket.
The Test was also Virat Kohli's first since the birth of his second child made him miss India's 4-1 victory over England at home earlier this year.
Kohli scored just six and 17.
Bowlers led by Jasprit Bumrah handed India an early advantage after they bundled out Bangladesh for 149 in their first innings.
India are looking to extend their lead at the top of the World Test Championship rankings in a fresh Test season of 10 matches.
Bangladesh came to Chennai fresh from a landmark series win in Pakistan but they have still never beaten India in Tests.
The two teams now head to the northern Indian city of Kanpur for the second Test starting on Friday.