Steve Smith on his way to his 11th test century against India. Photo: Photosport
Australia captain Pat Cummins was also among the runs, the tailender falling for 49 as he and Smith combined for a potentially decisive 112-run partnership after resuming on 311 for six at the Melbourne Cricket Ground.
Having scored a drought-breaking 101 in the third test in Brisbane, Smith was unbeaten on 139, with tailender Mitchell Starc on 15 at the break.
India's bowlers had taken four wickets after tea on a scorching day one to check Australia's advance but they let the game drift in cooler, overcast conditions on the second morning.
Smith and Cummins were barely tested as they racked up 60 runs by the drinks break, smashing the second new ball around the ground.
Smith brought up his 34th test century, and second for the series, with a crisp, off-drive for four off Nitish Kumar Reddy.
India quick Mohammed Siraj's miserable test continued as runs piled up from his bowling and home fans jeered when he was inserted into the attack or fielded the ball.
Siraj, cast as India's villain since giving Travis Head a send-off in the Adelaide test, sent two bouncers soaring over Rishabh Pant's gloves for five byes each.
Hooked for six and smacked for four in successive balls by Smith, Siraj finished the session still wicketless in the test at the cost of 115 runs.
Ravindra Jadeja alone gave Indian fans some cheer when he denied Cummins a fourth test half-century, the Australia paceman well caught by Reddy in the covers when swinging for the fences.
India's relief was shortlived, though, as Starc kept the scoreboard ticking over, smashing Bumrah for a six over the long-on fence.
India's players wore black armbands as a tribute to the nation's former Prime Minister Manmohan Singh, who died on Thursday at the age of 92.
The five-match series is tied at 1-1, with the final test to come at Sydney.
-Reuters
