Joss Buttler (76) and Jake Ball (31) raised a 54-run stand for the ninth wicket to frustrate India, who enjoyed success early in the morning session with three quick wickets.
England added 112 runs to their overnight total after beginning the day at 288 for five.
Off-spinner Ashwin bagged six for 112, his 23rd five-wicket haul in 43rd game, while left-arm spinner Jadeja claimed 4 for 109.
Buttler was the last English batsman to be dismissed for 76, the second-highest scorer after the 112 made by debutant opener Keaton Jennings. Before being bowled by Jadeja he faced 137 balls and hit six fours and a six off Ashwin.
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Jadeja had grabbed two out of three wickets in the first session - sending back Chris Woakes (11) and Adil Rashid (4) - after Ashwin had given the first break for the home side with the dismissal of overnight batsman Ben Stokes for 31.
Indian openers Rahul and Vijay started confidently against the pace attack of the visitors who tried to use the short ball to unsettle both without success.
Vijay started with a superb drive past bowler Woakes while Rahul also played pleasing drives - a back-foot punch square of the wicket off leggie Rashid catching the eye.
But he went for an ambitious drive on the track offering copious spin against Moeen Ali and was bowled through the gate for 24 after a stay of 41 balls. England had brought on their double spin attack after only seven overs.
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