At stumps, England were in deep trouble at 78 for four, still 56 runs in arrears and only six wickets at their disposal.
Earlier in the day, Ravindra Jadeja smashed his way to a career-best 90 while Ashwin hit 72 as lower middle-order once again put up a power-packed performance to score a commendable 417 in the first innings, thereby giving India a healthy 134-run lead over England.
A four-day finish with a 2-0 lead is looking imminent for India.
Having set up the match with a well-compiled half-century with the bat, Ashwin (3/19 in 12 overs) came back to remove rival captain Alastair Cook (12), Moeen Ali (5) and Ben Stokes (5) as India tightened the noose around England. Jayant Yadav (1/12 in 6 overs) then came in to remove first innings half-centurion Jonny Bairstow (15) before the close of play.
England's No 1 batsman Joe Root (36 batting, 101 balls) stands between India and victory.
While he may not be 100 per cent fit but Ashwin looked like getting a wicket with most of his deliveries. On a pitch where Moeen Ali and Gareth Batty looked ordinary, Ashwin, with his length and deception, looked more potent.
It seemed Ashwin has been successfully able to play on Captain Cook's mind as he again tried in vain to indulge in a game of survival.
Cook survived a couple of close calls on DRS but then Ashwin bowled one that angled in with skipper playing down the wrong line only to find his bails clipped off.
Moeen, batting at No 3, didn't reach to the pitch of the delivery and his forced chip shot could not clear Jayant Yadav at mid-on, who ran a few yards back to complete a reasonably simple catch.
The highlight of the first two sessions was Jadeja's 90 off 170 balls that had 10 fours and a six. His partnership of 97 with Ashwin is likely to have a great impact in the final context of the match.
Not to forget the 80-run stand he shared with rookie Jayant (55, 141 balls, 5x4), who also helped himself to a maiden half-century in Test cricket.
Jadeja also eclipsed his previous best of 68 against the same opposition at Lord's in 2014.
Debutant Jayant, India's 'find of the series' once again impressed with his fighting qualities as his gutsy innings ensured that India scored 400-plus for the third consecutive time in the series.
For the record, no visiting team has won against India after having conceded 65-run lead in the first innings. The last time it happened was 52 years ago, back in 1964 when Bob Simpson's Australia won after conceding a 65-run first innings lead.