It was the second time in the match that Ashwin had dismissed Cook, England's all-time leading Test run-scorer, this way.
He then struck several stylish attacking shots, including a classic cover-drive for four off Stokes and a lofted six off leg-spinner Adil Rashid.
England definitely won that session, but will they end up ruing those two drop off Kohli?
England were all out in their first innings for 287 early on Thursday.
After a first day which saw Joe Root win the toss and elect to bat but witness England finish at stumps on 285 for nine, the hosts were looking to perform much better on day two at Edgbaston.
Sam Curran was England's hero at Edgbaston on a day when Ben Stokes claimed his 100th Test wicket. The right-hander thanked his lucky stars as he was dropped twice on a score of 21 and 51 by Dawid Malan at slip. People think that I'm lying, but I genuinely have no idea what people are saying.
In fear of being bowled out to leave England well ahead, Kohli took over the task of controlling the innings. However, the prized wicket of Alastair Cook late in the day put the smile back on Kohli's face.
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While trying to steal a double run, Virat Kohli found him just short of the crease.
India have always been criticised for their poor close catching but England, with the tourists still on 100 for five, dropped two slip chances of their own, with Malan reprieving Kohli off Anderson.
Lokesh Rahul dispatched his first ball to the boundary but dragged his second from Curran on to his stumps.
That was when Sam Curren was thrown the ball and in the spate of eight deliveries the left-arm pace ace got three wickets.
Stokes, introduced after lunch, showed why he is such an important part of this England side with an aggressive spell.
Kohli was one of two players, along with David Warner, to record twin centuries in that Adelaide Test.
England will hope Jos Buttler will be able to bat on Friday after he went to the hospital during the lunch interval for an X-ray on his left middle finger, which he injured while fielding. And I had total clarity that we are going for the target.