After taking two Australian wickets for just 47 runs in the morning, the Indians took three wickets, including that of a determined opener Matt Renshaw (60), late in the post-lunch session to come back into the match.
Jadeja, who had picked up a wicket in the morning session, bagged two more, including that of Renshaw, in nine overs while conceding 19 runs.
At the end of the second session, Jadeja's figures were three wickets for 32 runs in 13 overs, a bowling performance which helped India to bounce back into the game.
Australia could muster 76 runs while losing three wickets in 35 overs in the session. Shaun Marsh was batting on 38 from 127 balls at the break.
The Indians toiled hard for more than 20 overs in the second session without any success with young opener Matt Renshaw and Shaun Marsh showing tremendous application on a turning track for a 50-plus partnership.
The Australian duo's doggedness looked like taking away the momentum from the fired-up Indians who showed a lot of intent today and the visitors were inching towards the home side first innings total of 189.
Peter Handscomb (16) and Mitchell Marsh (0) were out in the space of 3.2 overs. Renshaw's 60 came from 196 balls and he hit five fours and a six.
Australia now trail by 26 runs with five first innings wickets in hand on a difficult Chinnaswamy Stadium pitch where run-making has been extremely hard.
Renshaw, who dropped anchor to build a solid innings, took his time to score runs. He reached to his third half century when he clipped Ravichandran Ashwin through mid-wicket for a couple of runs.
Jadeja had the last laugh as he forced Renshaw, who had belted the same bowler over his head for a magnificent six, to come outside the crease to play the ball. The batsman missed it completely and Wriddhiman Saha dismantled the bails before the opener could get in.
Jadeja then removed Peter Handscomb, after the batsman scored 16 runs of 30 balls with two boundaries. He came down the track and tried to flick it but failed to get contact as the ball went straight towards Ashwin at mid-wicket.
Earlier, India removed dangerous opener David Warner and in-form captain Steve Smith cheaply as Australia reached 87 for 2 at lunch.
Warner (33) and Smith (8) fell to Ravichandran Ashwin (1/22) and Ravindra Jadeja (1/11) respectively as the Indian bowlers, especially the spinners, made it difficult for the Australians to score runs on a turning track which had a lot of cracks.
Ashwin, who opened the bowling with Ishant Sharma, gave India the breakthrough in the sixth over of the day and third of his own as a gem of delivery knocked off Warner's off-stump as the batsman was completely beaten by the extravagant turn of ball after landing outside the leg. Warner's 33 came from 67 balls and contained three fours.
Opener Renshaw, who was dropped by Indian captain Virat Kohli at slips off Umesh Yadav's bowling, was batting on 40 off 144 deliveries at the lunch break after starting the day on 15.
Australia, who were 40 for 2 overnight, could only add 47 runs from 29 overs while losing two important wickets.
India, who were shot out for a paltry 189 in the first innings, showed a lot of intent and they were fired up for most part of the morning session.
Ishant and Smith were involved in some theatrics with the India pacer making faces on quite a few occasions to the visiting captain after his shout for an LBW was turned down by the umpire. Kohli was also seen enjoying the moment as he wore a smile from behind to what Ishant was doing.
Smith looked like amused initially but later retorted in his own way. The Australian captain also survived a close LBW decision. India asked for a DRS referral but to no avail.
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