The hosts were eventually all out for 210 to hand India a 2-1 lead in the five-match series.
The final match will be played in Manchester from September 10.
Bumrah was exceptional with his in-swinging balls and teasing yorkers while Jadeja exploited the rough patches on the track to tilt the game in India's favour.
England lost six wickets for 62 runs in the second session and were all out in post-tea session.
Bumrah dismissed Ollie Pope (2) and Jonny Bairstow (0) while Jadeja saw the back of Haseeb Hameed (63) and Moeen Ali (0).
Shardul Thakur got the key wicket of rival skipper Joe Root (36) while Umesh Yadav dismissed Chris Woakes (18), Craig Overton (10) and James Anderson (2).
Brief Scores:
India: 191 and 466
England: 290 and 210 in 92.2 overs. (H Hameed 63, R Burns 50; U Yadav 3/60, S Thakur 2/22, J Bumrah 2/27, R Jadeja 2/50).
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Dhanbad (Jharkhand) (PTI): At least four workers died after being buried under coal slurry in Jharkhand's Dhanbad district on Saturday, a police official said.
The incident took place at Moonidih coal washery in the command area of Bharat Coking Coal Limited (BCCL).
"Bodies of all four workers were dug out of debris during a rescue operation," Putki police station in-charge Waqar Hussain told PTI.
The incident took place when coal slurry was being loaded into trucks by workers, during which a large chunk of slurry fell and trapped several workers underneath, officials said.
The deceased have been identified as Manik Bauri, Dinesh Bauri, Deepak Bauri, and Hemlal Gope.
Meanwhile, the family members of the deceased and local villagers placed the bodies in front of the washery gate and began a protest.
They demanded compensation, jobs for dependents and action against those responsible for the incident.
Police and administration officials are trying to pacify the protesters, an official said.
