Jadeja returned figures of 5/124, the eighth five-wicket haul of Jadeja's Test career and the fourth this season.
Fast bowler Umesh Yadav also bowled well for figures of 3/106 while star off-spinner Ravichandran Ashwin also bagged a wicket.
Skipper Steven Smith played a captain's innings for Australia and remained unbeaten on 178.
He hit 17 boundaries during the 361 balls he faced.
Glenn Maxwell, who returned to the Australian Test side after a lengthy period, scored his maiden century in the longest format of the game and put on a 191-run stand with Smith to help the visitors to a strong position after losing early wickets on the opening day.
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