Smith held his end as Jadeja led India's fightback with an eighth five-wicket haul in Tests. Glenn Maxwell (104) also contributed to the formidable first innings total with a hundred in his comeback game.
By tea, India openers Murali Vijay and Lokesh Rahul had seen off the Australian pacers scoring 20 runs in eight overs.
On a placid wicket at the JSCA Stadium's maiden Test, super Smith looked unstoppable on way to his 19th century. He continued from where he left off after resuming on an overnight 117 to surpass the highest score by an Australian captain in India, eclipsing Michael Clarke's 130.
The skipper batted for more than eight and half hours facing 361 balls with 17 boundaries and was involved a series-high 191 partnership with Maxwell in an emotional Test comeback after more than two years.
Shedding the T20 specialist tag, Maxwell built innings with tremendous restraint and punished the loose deliveries in his 185-ball knock.
Smith was also involved in three of the four half-century stands as Australia posted the highest total of the series.
It was Indian left-arm spinner Ravindra Jadeja who toiled hard for his 5/124, and his twin strikes in three balls before lunch gave the home team some much needed momentum going into the break.
After Maxwell's departure, Matthew Wade notched a 50-ball 37 in a 64-run sixth wicket partnership with Smith.
But Jadeja put the brakes on dismissing Wade and Patt Cummins (0) 10 minutes before lunch to infuse some energy in the Indian camp.
Introduced in the sixth over, Jadeja bowled a non-stop spell and took all the three wickets in the first session.
With Ravichandran Ashwin (1/114) returning wicketless so far on day two, Jadeja had to take the bulk of the workload as the left-arm spinner bowled 49.3 overs.
Jadeja completed a fine run-out of Josh Hazlewood by backflicking Rahul's throw to bowl out Australia for in 137.3 overs.
Indian camp looked dispirited in absence of skipper Virat Kohli who remained away, recovering from a shoulder strain after his awkward dive yesterday.
Kohli's is out of the field for six hours and 40 minutes, since 39.1 over in the post-lunch session yesterday when he landed awkwardly, trying to save a boundary off Peter Handscomb at mid-on.
His absence from the field however would not affect his number four batting position with this being an external injury.
Kohli's deputy Ajinkya Rahane led the team and did some smart bowling changes but they struggled to get the first breakthrough of the day after the Aussie resumed on 299/4 with Smith and Maxwell holding fort.
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