Joe Root (14) held the key to England's second innings, and eventual course of the game, but Ashwin etched out the big wicket eight overs later.
The 20-year-old left-armer proved he can be a major weapon if the ball is swinging.
India will be hoping Kohli, who scored a brilliant 149 on Thursday, can produce another heroic performance as they will need to pull off their highest fourth innings chase in England if they want to take a 1-0 lead in the five match series.
Playing a skippers' knock, Kohli now stands between victory and defeat for India. The Yorkshireman's round of broadcast interviews to clear the air were most welcome.
Left-hander Broad could only edge an away moving ball from Ishant as it landed at the hands of Shikhar Dhawan at first slip. "If we can bowl well and take a couple up top, we will hopefully win".
North Korea: Spy images pick up 'new activity' at missile site
Lewis's group also published images of a large industrial facility that some US intelligence analysts believe to be the Kangson uranium enrichment plant.
Virat Kohli's masterclass century defied England and dragged India back into the contest on a gripping second day of the first Specsavers Test at Edgbaston. So far in this match, Curran has put his imprint on two of them, with the ball on the second day and with the bat on the third: the mark, in other words, of a genuine all-rounder, and one who clearly has a sense of occasion. He broke the budding 21-run partnership between him and Dawid Malan (20) as Rahul held another excellent, low catch at leg slip.
Lokesk Rahul took both catches.
Rahane caught first Malan at fourth slip in the 27th over. Then in the last over before lunch, Sharma struck twice to dismiss Bairstow, caught at first slip, and Ben Stokes (6), caught at third slip, in the space of three balls. "The good thing was I had overs behind me".
Mohammad Azharuddin, one of India's greatest fielders, feels India's lacklustre slip fielding on Thursday in Birmingham was simply a case of not practising enough.
Curran, who bats left-handed as well as bowls, brought up his maiden Test fifty off a mere 54 balls in supreme style by lofting Sharma over extra-cover for six.