The in-out fields allowed Buttler to take strike for up to five balls in an over, and England could pick up 33 runs for the last wicket before Buttler miscued a big hit off Bumrah to long-on. Before that Rahane, who got his first half-century in more than a year, found Cook standing at first slip taking a sharp one-handed reflex catch off Stuart Broad's (1/64 in 21 overs) bowling.
Ben Stokes, returning to the side after being cleared of affray, was particularly ineffective, returning 0-54 from 15 overs.
Not that the selection of Stokes has cost England the Test and turned Sam Curran into a world-beater but it has clearly disrupted the equilibrium and momentum of a team who had looked so dominant at Lord's without him.
India bowled out England for 161 in their first innings at tea on the second day of the third cricket Test on Saunday. An uppish drive from Cook between cover and point in the first over after lunch had raised England's 50 - and given Cook his highest score of the series - but would have also encouraged Ishant Sharma.
While the India top order showed some improvement against the moving ball, the visitors were still in danger of capitulating when Kohli was joined by Rahane.
Kerala floods: UAE provides relief assistance
Roads and 134 bridges have suffered damage, isolating remote areas in the hilly districts of the state which are worst affected. We must all contribute to help the distressed and the affected people.
20 year old debutant Rishabh Pant flipped Rashid for a six to score first worldwide runs and took India's score to cross 300 runs. First, he had Root caught at second slip with Rahul getting his fingers under the ball in time for the TV umpire to rule in his favour.
He dismissed Cook for the 10th time in Test cricket, caught behind in the 12th over after the left-hander was dropped by Pujara at first slip two balls earlier.
It took the introduction of Woakes, man of the match at Lord's, to improve England's morning. Shami tosses up the length delivery and Broad gets underneath it. Shami OUT on 3.
India has had everything to lose on the brink of opening the third Test match at Trent Bridge, Nottingham. Woakes removed Dhawan, Rahul and Cheteshwar Pujara (14) in quick succession as India from 60 for no loss went into the lunch at 82 for 3. A high-quality spell of sustained in-swing from both Ishant and Bumrah continued, with Joe Root and Jonny Bairstow hurried onto the back foot. In his next over, Broad bowled R. Ashwin with a huge in-swinger. He was curious to see his team bat after India put a substantial total on the board.
England bowler Stuart Broad appeared to suffer a nasty sting when running in to bowl on Saturday afternoon when a wasp, or something similar, flew into his mouth and landed on his tongue.