Shikhar Dhawan (26) and Cheteshwar Pujara (15) survived a late onslaught on Friday, remaining unbeaten at the crease as India closed the day 71-1 at the Gabba, with Murali Vijay (27) the only wicket to fall, bowled by Mitchell Starc.
Vijay was undecided as to whether to play or leave and he paid the price as paceman Starc sent the opener packing in the 11th over.
That wicket threatened to derail the tourists, who were outplayed by Australia throughout on day three.
Australia managed to overhaul India's first-innings total of 408, reaching 505 thanks to another Test century from captain Steve Smith. Smith's 133 followed his 162 first-innings knock from the first Test as his fine form with the bat continued.
After opening the day 221-4, Australia lost quick wickets.
Mitchell Marsh and vice-captain Brad Haddin were dismissed within 10 overs of each other as India reduced Australia to 247-6.
Marsh was the first wicket to fall, deceived by Ishant Sharma (3-117) for 11 runs.
Haddin followed Marsh back to the pavilion shortly after, caught by Pujara off Varun Aaron (2-145).
But Smith - deputising for the injured Michael Clarke - combined with tailender Mitchell Johnson (88) to help Australia wrestle momentum back in their favour.
Smith brought up his century - his sixth hundred in 13 matches - as Australia went to lunch 351-6.
The blitz continued after the break, with Smith and Johnson putting on a 148-run partnership from just 26 overs.
Johnson was eventually dismissed by Sharma just 12 runs short of what would have been a memorable century.
Sharma claimed the wicket of Smith five balls later, although Starc (52), Nathan Lyon (23) and Josh Hazlewood (32 not out) - the hero on day two - made significant contributions at the bottom of the order.