Dawid Malan drops Virat Kohli off Jimmy Anderson. Kohli was the last Indian wicket to fall, just one shy of 150.
Cook fell to a wonderful piece of bowling by Ravi Ashwin, India's only spinner here but brought into the attack for just the seventh over.
Batting with Ishant Sharma he added 48 for the ninth wicket, before Sharma (5) went LBW to Adil Rashid.
His last-wicket stand of 57 with Umesh Yadav - of which the number 11 contributed only one run - was full of clean hitting from Kohli, who launched Rashid over long-on for six before finally falling as he slapped the leg-spinner to Stuart Broad at point.
He continued to punish the England bowlers to notch up 22 boundaries and a six during his 225-ball knock. Yes, he was dropped twice but that does not take away from the fact Edgbaston got to witness a master at work.
Root did at least bag one notable career milestone, displacing Alastair Cook as his country's quickest to 6,000 Test runs when he reached 40.
India headed into the Tea break on Day 2 at 160 for 6.
England swing bowler Sam Curran took three wickets in eight balls before lunch - removing Murali Vijay (20), Lokesh Rahul (4) and Shikhar Dhawan (26) - to reduce India to 3-59, before the tourists were given a testing first hour of the afternoon session against a ball that swung around. It brought out Kohli who was booed on his walk to the crease. The first should have been taken, the second could have been. That left Kohli and Co. on 100 for four. India were at a hard position at 169/7 when Ashwin went back to pavilion after just 10 runs. Low-scoring, as the most exciting Tests are.
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.
Once Hardik Pandya was dismissed on a beautifully swinging delivery from Sam Curran, it looked as if the Indian innings was nearing its end.
Ben Stokes had his head in his hands after Kohli was dropped.
But playing in just his second Test, Curran made a huge impact, tearing through India's top order after they made a fine start to their first innings.
Early wickets, especially that of Joe Root, will be a crucial factor for the visitors if they are to restrict England to a modest total. It's good to have those little moments within things.
Vijay was solid as usual, leaving the ball well, while Dhawan looked to play down the ground.