In doing so, Stokes become the eighth Englishman to complete the double of 2,000 runs and 100 wickets in Test cricket.
From a position of relative strength at 216 for 3, England lost their next six wickets for 69 to reach the close on a dicey 285 for 9.
On a typical day of Test cricket with the ball doing a bit, spectators were treated to the ebbs and flows of the five-day format and a top drawer contest between Virat Kohli and Jimmy Anderson.
It was Kohli at his most brilliant and daring, when he departed for 149, caught at cover off the bowling of Rashid, he had got India to only 13 runs behind England's total, and scored over half his side's runs.
Only Cook fell in the first session, his front-foot defence defeated by a flawless off-break from Ashwin - repaying his introduction in only the seventh over, despite being India's sole spinner here, with telling drift from round the wicket before the ball turned and dislodged the off-bail.
He dominated a last-wicket stand of 57 with Umesh Yadav, who made just one, with India just 13 runs adrift at 274 all out.
Making the most of the two dropped catches by England at 21 and 51, Kohli let out a huge roar in celebration after belting the ball off Ben Stokes for a boundary to bring up his century.
Root was extremely disappointed to fall 20 runs short of his 14th test century, but he achieved a notable milestone, displacing Alastair Cook as England's quickest to 6,000 runs in this format.
Jennings survived a scare on nine when he edged Ishant Sharma, but Ajinkya Rahane failed to hold on at fourth slip as he dived to his right across Kohli.
From then on, he added the next 49 runs in brisk pace knowing they had only one wicket in hand.
The opener managed only to push the ball down into his crease off back-foot defence, then onto his foot before it trickled back onto the base of the stumps. "He celebrated, and that's cool", Jennings said at the end of day's play, playing down the incident.
Speaking after his Headingley innings, Root had admitted he "would not hear the end of it", adding that his own team-mates had been ribbing him incessantly for the gesture.
"You can't say that we will miss an extra spinner", said Ashwin. Yes, he was dropped twice but that does not take away from the fact Edgbaston got to witness a master at work.