Smith, comfortably the leading scorer of the series, made 111 as he and David Warner, who scored 56, added 134 runs for the second wicket to help Australia dominate the morning session after opting to bat.
Left-arm wrist-spinner Yadav, an inspirational selection in India's bold move to go with five bowlers, led the hosts' strong comeback in the post-lunch session when five wickets tumbled for 64 runs.
Matthew Wade made 57 down the order to help Australia reach 300 before the tourists folded leaving India to bat the final over of the day, a maiden one from Josh Hazlewood.
Wade conceded Australia lost an opportunity to post a bigger total.
"(Australia were) one for 140, so after lunch you hope to push but credit to the Indians who bowled really well through the middle session," he told reporters.
"We had to find a way to grind out 300. To get there in the end was a good effort."
Openers Lokesh Rahul, who faced all six deliveries from Hazlewood, and Murali Vijay will hope to give India a strong start when they resume on Sunday.
The hosts received a jolt even before a ball was bowled when regular skipper Virat Kohli was ruled out of the match with a shoulder injury he had sustained in the drawn third test in Ranchi.
Bhuvneshwar Kumar, replacing fellow paceman Ishant Sharma, swung the first ball of the match to induce an edge from Warner but Karun Nair spilled it at third slip.
India did not have to wait long for the breakthrough though.
In the next over, Umesh Yadav pushed one through Matt Renshaw's gate and pegged back his off-stump to dismiss the opener for one.
Smith and Warner laid the foundation for a big first innings total with a century partnership during which Smith's characteristic fluency contrasted Warner's scratchy knock.
Warner brought up his first fifty of the series after Smith had reached his own, before Kuldeep led India's fightback after lunch with brilliant display of wrist-spin bowling.
The 22-year-old generated extra bounce and the ball flew off the shoulder of Warner's bat en route to India's stop-gap skipper Ajinkya Rahane at slip.
Umesh dismissed Shaun Marsh for four before Kuldeep (4-68) returned to further torment the tourists.
The Uttar Pradesh player disturbed Peter Handscomb's stumps and then bamboozled Glenn Maxwell with a brilliant googly to peg back Australia.
Smith brought up his 20th test century in 150 balls to steer Australia past the 200-run mark before edging Ravichandran Ashwin to Rahane in the slip.
Smith faced 173 balls during his composed knock, hitting 14 boundaries.
Wade and Pat Cummins, who made 21, defied the Indian bowlers for nearly 13 overs before being separated.
"All four wickets are special but I guess the first wicket (of Warner) was important from the team's point of view," Kuldeep said.
"They did not take a chance against me and were largely content taking singles. I didn't face any problem."
The four-test series is level at 1-1.
(Editing by Pritha Sarkar)
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