India, set a record 444 to win, resumed on 164-3. But they collapsed to 234 all out, losing seven wickets for 70 runs inside 24 overs before lunch on the fifth day.
Australia now need just five more wickets on the fifth day to capture the one major men's global title that has so far eluded them.
For the Aussies, the 2023 ICC World Test Championship final can be a distraction ahead of the Ashes, India hardly got a week to breathe after the IPL, but India have a tough game ahead against the tunnel-visioned Australians.