The tourists lead the series 2-1 and declared their first innings on 622-7.
Cheteshwar Pujara was finally out for 193, while Rishabh Pant hit his second Test century in reaching 159 not out.
Captain Virat Kohli declared an hour before stumps after Ravindra Jadeja was out for 81. Usman Khawaja and Marcus Harris then guided Australia to 24-0.
However, India should have made an early breakthrough when Khawaja edged a Mohammed Shami delivery behind but wicketkeeper Pant dropped a reasonably straightforward chance.
Pujara, who was 139 not out overnight and has scored three centuries in the series, looked set to score a fourth double century but was caught and bowled by Nathan Lyon after a nine-hour, 373-ball knock.
Pant and Jadeja then hammered home India's advantage with a 204-run partnership in 37 overs, the former reaching his century off 137 balls, the first India wicketkeeper to do so in Australia.
Lyon, who took all three wickets to fall on day two, eventually bowled Jadeja and finished with figures of 4-178.