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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Dubai/Abu Dhabi: Residents and visitors across the United Arab Emirates received a fresh emergency alert on their mobile phones stating that the situation in the country is currently safe.
The message, issued by the Ministry of Interior (MOI), thanked people for their cooperation and reassured them that conditions were stable.
“Thank you for your cooperation. We reassure you that the situation is currently safe. You may resume your normal activities while continuing to remain cautious and take the necessary precautions, and to follow official instructions. (MOI),” the alert read.
The notification was sent in both Arabic and English through the country’s emergency alert system.
The advisory comes after earlier alerts warning of potential missile threats amid rising regional tensions. Authorities have urged the public to stay cautious and follow official guidance.
