The Australians were struggling at 247 for six before staging an amazing comeback to pile up an imposing 505 in the first innings riding on Steve Smith's second successive century and useful contributions from the tailenders.
Smith (133) became the ninth Australian to score a century on his captaincy debut as the hosts wriggled out with Mitchell Johnson (88) and Mitchell Starc (52) adding valuable runs down the order at the Gabba.
The last four Australian wickets added 258 runs to virtually take the game from India, who looked like taking the first-innings lead at one stage.
Resuming the day on overnight 221 for four with Smith unbeaten on 65, Australia lost Mitchell Marsh for the addition of just 11 runs to Ishant Sharma (3/117) before Varun Aaron (2/145) had Brad Haddin caught at short leg.
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This was Smith's second consecutive hundred in the series, having reached the three-figure mark in the opener in Adelaide.
With the two batsmen going strong, Australia went to lunch at 351 for six, and consolidated their position thereafter to be sitting pretty at 503 for nine at the tea break.
However, the Indians wrapped up the innings soon after tea with last man Starc being bowled by Ravichandran Ashwin (2/128), bringing some relief to the visitors who toiled in the first two sessions.