India, who have not lost a test series at home since 2012, finished day two on a commanding 421-7 in their robust reply to England's middling 246 in the first innings.
Jadeja was on 81 at stumps having raised 63 runs with Axar Patel who was batting on 35.
After India resumed day two on 119-1, England opened with part-time spinner Joe Root, who dismissed the dangerous-looking Yashasvi Jaiswal (80) in his first over.
Jaiswal hit Root's second ball for a four but, two balls later, offered a high return catch to Root, who leapt to pouch the ball.
"It would have been amazing to get a hundred here," Jaiswal said though he did not regret playing that shot against Root.
"This is my first test in India and I was just thinking how can I contribute and do well for the team."
Rahul got a reprieve when Ben Foakes grassed a tough chance behind the stumps after the batter, yet to open his account, had edged Root.
Root was unlucky again when Shubman Gill miscued a shot but Ben Stokes, stationed at mid-off, lost sight of the ball against the sun.
Root was taken off the attack after four overs in a move as surprising as England's decision of not bowling him on Thursday when Jaiswal was toying with the England spinners.
Tom Hartley had particularly suffered at the hands of Jaiswal but the left-arm spinner put that agony behind him and dismissed Gill (23) for his first wicket in international cricket.
Rahul smacked two sixes in a Rehan Ahmed over to put India in the lead and forged half-century partnerships with Shreyas Iyer (35) and Jadeja to consolidate India's position.
Leg-spinner Ahmed removed Iyer with Hartley taking the catch in the deep.
The roles were reversed as the English duo combined again to dismiss Rahul, who threw his bat in disgust after pulling a Hartley half-tracker to Ahmed when a hundred seemed there for the taking.
Jadeja, who added 68 runs with Srikar Bharat (41) for the sixth wicket, celebrated his eventful half-century twirling the bat in his signature sword-dance style.
The all-rounder was twice adjudged out - first caught at short leg off Jack Leach and then lbw to Root - but both decisions were overturned on review.
Jadeja was also involved in an almighty mix-up that led to Ravichandran Ashwin's run-out after both batters ended up at the same end.
England bowling coach Jeetan Patel was happy with the way their spinners bowled on a "tough day".
"Just because it's spinning doesn't mean it makes the game easier. In fact, sometimes it becomes harder because there's so much expectation," he said.
"Our guys learned from this yesterday and they bowled better today...they'll keep getting better throughout the series."
Leach was used in short spells after the left-arm spinner bumped his knee twice in two days, Patel added.
