The first of three wickets to fall for eight runs as he side slipped 3-216, Root's misfortune was accompanied by a full-house "send-off" from his opposite number Virat Kohli.
Buttler was injured diving to his left at gully in an attempt to catch Kohli off Anderson, the ball appearing to clip his fingertip, though in a boost for England he was cleared of any major damage. The second highest scorer in the innings was Shikhar Dhawan's 26.
Root looked imperious, though, and punished any bad balls with four boundaries coming off his bat before lunch in a 57-run partnership with Jennings.
Just four runs were added to Indian total when India lost KL Rahul. who scored mere four runs. It is a manifesto of what they are going to achieve, by bending opponents to their will; and, unlike politicians, they usually adhere to it. Kohli announced that he can score red-ball runs in England in spite of James Anderson's stated belief.
His experience in the County Championship has helped Ravinchandran Ashwin vary his pace and simplify his bowling action for English pitches, the off-spinner said after his 4/60 on the first day of the Edgbaston Test.
Joe Root became the quickest England batsman to pass the milestone of 6,000 Test runs against India at Edgbaston.More news: New indicators show North Korea potentially working on missiles, Washington Post reports
A match, and series, on a knife-edge.
The session got even better for India as Ashwin bowled Alastair Cook for a duck, to leave the tourists on nine for one.
Teammates congratulate England's Sam Curran for the dismissal of India's Lokesh Rahul during the second day of the first test cricket match between England and India at Edgbaston in Birmingham, England, Thursday, Aug. 2, 2018.
Root top-scored with 80 before falling run out.
It may have taken Broad a while to get Rahane, an average of 46.3 balls per wicket, but he still picked him up cheaply - twice caught by keeper Matt Prior and a screamer at third slip by Gary Balance in the fifth test.
India had got off to a solid start in the morning as openers Murali Vijay and Dhawan chalked up a half-century partnership but the visitors were then rocked by three swift strikes by left-arm swing bowler Sam Curran.