Left-arm spinner Jadeja first cut short Alastair Cook's stay at the crease when he was one shy of a half century, followed that with the dismissal of Keaton Jennings and then sent back Joe Root to leave England at a spot of bother at 126 for three.
The situation got worse for the visitors when they lost Jonny Bairstow, sent back by a Ishant Sharma, who looked pretty sharp and thereafter tested Ben Stokes with deliveries that got off the wicket.
Jadeja, who pulled off a brilliant catch at midwicket to pull the curtains on Bairstow's brief stay in the middle, had impressive figures of 3/38 before the start of the final session.
Moeen and Stokes' partnership had consumed 12 overs by tea, and will have settled English nerves a bit.
Even though the hosts looked threatening, England took solace from the fact that the pitch remained pretty flat and could hope to avoid a 0-4 drubbing even if India had set ultra attacking field placements.
Jennings offered a return catch to Jadeja in a soft dismissal, while Root was out lbw after he went for a sweep and failed to connect.
Virat Kohli went for a review after the on field umpire thought otherwise, and the India skipper was right as replays showed the full ball hitting the leg stump.
(REOPENS DEL 15)
Earlier, England got through to lunch unscathed, reaching 97 without suffering an early setback, as India looked for a breakthrough.
Trailing by 270 runs after conceding a huge 282-run first-innings lead, an innings defeat was not out of question when the English openers made their way back to the pavilion at stumps on the fourth day at the MA Chidambaram Stadium.
However, skipper Cook and Jennings stood firm and succeeded in negotiating the Indian bowlers in the first session of play on what is by far the best batting surface in the series.
Luck was on England's side in the first session as Cook got a life three overs into the day's proceedings. The bowler to suffer was off-spinner Ravichandran Ashwin as wicketkeeper Parthiv Patel failed to latch onto an outside edge from the left-hander's willow.
As the ball turned away from Cook, Parthiv moved to his left but the ball brushed the gloves and fell in front of slip. The ball would have gone straight to Virat Kohli if Parthiv had not moved to his left. Cook was on 4 then.
Till lunch, even with fielders placed around the batsmen, they could not succeed though Ashwin should have had a wicket to his name.
Cook and Jennings had been watchful, showed the gumption to fight for a draw and though there was one clear chance, the pitch has nothing for the bowlers. England then trailed by 185 runs with all their wickets intact.
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