Jadeja, playing his first test of the series after being called in place of the injured Ravinhandran Ashwin, added to his haul of four first-inning passes by scoring highest with 86 not in a total of India's first innings of 292.
England, who led by 40 runs in the first inning, has struggled for a long time to find an opening mate for Cook, with 12 batters given a chance at work since Andrew Strauss retired six years ago.
And before his coming from Sri Lanka, England may now be looking for two starting pitchers instead of one after Keaton Jennings completed a miserable series by playing 10 moves without a shot to Mohammed Shami on Sunday.
It was the second time in so many Tests that Jennings had been fired leaving the ball and wanted to say that he finished the series with only 163 runs with a minimum average of 18.
A carefree Cook, who has already batted for more than three hours in this possibility, hit 26 balls without scoring, but took advantage of a ball thrown to take Shami to the floor by four.
Moeen Ali, batting in number three, another of England's problematic positions, failed to demonstrate a similar patience.
The third member of all three of the best left-handers in England, Moeen drove lamely with Ishant Sharma at 14, only for the second, normally reliable, KL Rahul slip to drop the possibility of a high head.
Fortunately for India, Modeja was knocked down by Jadeja for 20 years trying to get the driver out of his left arm for rudeness.
But Root, batting in his favorite position of number four, showed his class with a four-stroke lead to Shami to bring the score to 100 for two.
– Anderson went frustrated –
A frustrating day for England's spearhead, James Anderson, saw him stay within walking distance of Glenn McGrath's grand record of 563 Australian test terrains, the most taken by a fast bowler.
Before the game began, the International Cricket Council announced that Anderson had received a 15 percent fine for "speaking aggressively" to referee Kumar Dharmasena on Saturday after a review of lbw against Indian captain Virat Kohli. Follow the path of the star hitter. .
Kohli eventually fell to Ben Stokes by 49 points, strengthening a control of England in the game set on Saturday by Jos Buttler making 89 on his 28th birthday.
India again got into trouble with 174 for six, with Vihari 25 out and Jadeja undefeated with eight.
Vihari, who went through a couple of incidents near lbw that involved Broad when he was not at all, was increasingly confident in completing fifty in 104 balls, including six four and six.
But a seventh-round partnership of 77 ended when Moeen, whose hat-trick ended last year's Oval Test against South Africa, caused Vihari to be trapped by Ranger Jonny Bairstow by 56.
Jadeja completed a total of 113 balls, including seven legs and celebrated the milestone with a characteristic turn of the bat.
The fool Jennings then snatched a bat / pad opportunity when the last man, Jasprit Bumrah, passed the first ball to the leg runner Adil Rashid.
Jadeja, with 56 at that time, took advantage of Bumrah's pardon.
England took the new ball just for Jadeja to push Anderson directly on his head for six and hook Broad for four to the long leg.
But Jadeja, who made his highest score in the 90th test against England in Mohali two years ago, was less than a hundred when Bumrah ran out trying to keep the attack.
(With AFP entries)