Jadeja returned to haunt South Africa with the ball after the Proteas came out to bat for the second time in the match.
Ravindra Jadeja's four-wicket burst set India on course for a victory inside three days after a bruising day two in the low-scoring opening test against South Africa on Saturday.
India were in the box seat after bundling out South Africa for 159 at Eden Gardens where inconsistent bounce has been a bane for the shot-makers from both sides.
It was evident in India's reply too as they managed 189 to be left with a lead well short of their own expectations.
South Africa faltered in their second innings as well and were reeling on 93-7 at stumps.
Skipper Temba Bavuma led their fightback with 29 not out and with Corbin Bosch on one at the other end.
India were one batter short in the first innings after skipper Shubman Gill retired hurt with a neck spasm, having made four.
Off-spinner Simon Harmer (4-30) dragged South Africa back into the contest after India had resumed on their overnight score of 37 for one.
Washington Sundar (29) hit Keshav Maharaj for a six but could not carry on and was caught at slip off Harmer's bowling.
Gill opened his account with a four but immediately walked off the field rubbing his neck.
Returning from a foot injury that kept him out of the home series against West Indies, Rishabh Pant (27) had the South Africa players on their toes right after he walked in.
Pant was surprised by a leaping Maharaj delivery, which he guided towards slip where Markram was too startled to react in time and take the catch.
Pant rubbed salt into Maharaj's wound by stepping out to the next ball and hitting it for a six over mid-off.
The spinner found some solace when he had Rahul (39) caught at slip but Pant scored freely.
Bosch brought relief to the South Africa camp when he dismissed Pant caught behind with a bouncer.
Jadeja contributed 27 but lack of partnerships hurt India, who folded half an hour before the tea break.
Jadeja returned to haunt South Africa with the ball after the Proteas came out to bat for the second time in the match.
After Kuldeep Yadav got rid of Ryan Rickelton for 11, South Africa's frontline batters surrendered to Jadeja's (4-29) relentless left-arm spin.