Australia resumed on 12-3 after a devastating new-ball spell from Jasprit Bumrah and Mohammed Siraj late on day three - and that soon became 17-4 when the latter had Usman Khawaja caught behind off a top-edged pull.
Steve Smith was then superbly set up by Siraj, caught behind for 17 off one that straightened.
Travis Head (89) and Mitchell Marsh (47) counter-attacked but both fell in quick succession in the afternoon session to Bumrah and Nitish Kumar Reddy respectively.
Off-spinner Washington Sundar had Mitchell Starc caught at short leg and bowled Nathan Lyon, before a superb Nitish Rana slower ball deceived Alex Carey to seal the comprehensive win.
India must win three of the next four Tests to guarantee their place in a third successive World Test Championship final.
Australia need five wins across this series and a two-Test tour of Sri Lanka to reach the final.
The second Test in Adelaide starts on 6 December.
More to follow.