Kohli went on to score 149 and was batting on 43 not out in India's second innings score of 110 for 5 with the visitors still needing 84 more to win first Test. Anderson rued his side's poor catching and said England need to take their chances against a batsman of Kohli's calibre.
But it should have been even better for England with dangerman Virat Kohli and Hardik Pandya dropped in the slip cordon off successive deliveries.
"If you've to win a Test then everyone has to score runs". But when he was out for 51, England were on their way.
With the exception of Kohli, none of the Indian top order batsmen looked at ease against the bowlers, with Stuart Broad the pick of the attack with two wickets.
The skipper was downbeat after the match despite his 22nd Test ton. "Back in the day I used to think about playing in different conditions, different countries, but when you become captain it's about taking your team across the line".
Interestingly, no other bowler has dismissed Ben Stokes more than Ravichandran Ashwin. It's why he doesn't play white-ball cricket for India any more, because he tends to bowl negative leg-stump darts when he's under pressure.
England secured a 31-run victory in the series opener on Saturday and while Bayliss admitted he expects India to come back hard in the capital, he believes if the ball swings at Lord's it could be difficult for the tourists.
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But Stokes, who might not play the second Test owing to his court case, managed to nick out the edge England wanted. He was the top wicket taker from India in the first innings as he ended up with the figures of four for 62.
And he followed that up with a dashing 63, his maiden Test fifty, to give England a target worth defending after they had collapsed to 87 for seven in their second innings.
Here are the records broken in the first Test match at Edgbaston.
"Last night, [India's] opening spell could have really been the difference, but the boys didn't let me down at all", the England captain told BBC Test Match Special. The 31-run defeat is India's fourth-closest defeat and closest since 2000.
Dawid Malan will have been particularly relieved that England emerged victorious after twice flooring Kohli, on 21 and 51, in the cordon during the India skipper's century.
That sort of atmosphere is what it's about, that's what makes Test cricket so brilliant.
For all the blistering big-hitting of the white-ball game, the way the momentum shifted from one day to the next at Edgbaston, culminating in a gripping final session, underlined that nothing in cricket can beat the drama of a hard-fought Test.