The visiting team, who won the toss and opted to bat in the maiden Test hosted by this city, lost captain Alastair Cook for 21 and debutant Haseeb Hameed for 31 on either side of the drinks break.
The tourists then lost left-hander Ben Duckett (13) who was dismissed right at the stroke of lunch becoming Ashwin's second victim.
Joe Root was the unbeaten batsman on 35 during his 55-minute stay at the crease.
Off-spinner Ashwin accounted for the wickets of Hameed, whose dismissal also brought into play the Decision Review System (DRS) for the first ever time in a Test match played in this country, and Duckett, who had hit him for three boundaries in an earlier over.
Home town boy and left-arm spinner Ravindra Jadeja had earlier given India the first break at 47 by earning successfully a shout for leg before wicket against England skipper Alastair Cook.
Both the England opening batsmen were out leg before the wicket and England seemed to have erred with their DRS calls on both occasions - surprisingly not reviewing the verdict given against their captain and mainstay Cook and then going for a review of the decision against rookie Hameed.
In the morning, India's lengthy luck with the toss ended finally. Still they could have put England in early trouble but were let down by sloppy catching in the slip cordon.
Off the third ball of the series, Ajinkya Rahane put down India's scourge and rival captain Cook off Shami at gully after getting both palms wrapped around the ball by diving to his right.
Then it was the turn of Murali Vijay to let off debutant and right hander Hameed at first slip, a low catch, off Yadav when the teenage opener was 13 in a score of 24.
In between Cook lived dangerously, often flirting with the balls outside the off stump and edging some short of the slips or through the cordon for some runs.
After the 10th over, with England on 35 without loss, spin was introduced from both ends Ashwin and Jadeja bowling in tandem.
With there being hardly any hint of turn so early, the two slow bowlers were quite comfortably played by Cook and the debutant to take England to 47 without loss in 15 overs at the end of the first hour.
India, through home town boy Jadeja, struck the first blow and a big one at that with the first ball after the drinks break when Cook was trapped leg before as he tried to turn the left arm slow bowler to leg.
It looked worth the first instance of DRS call in Tests in India, but Cook had a word with his partner Hameed and walked back after scoring 21 in 47 balls.