Captain Pat Cummins declared Australia’s second innings closed at 89 for seven to give India a 275-run target as dark clouds gathered.
Australia may rage at the weather, having battled hard for a winning position while rain blighted four of the five days.
“Unfortunately a lot of rain, which you can’t do anything about. I’m proud of how the guys played,” said Cummins.
“We were ahead of the game. We just about ticked every box we could.”
Travis Head was named Player of the Match after scoring 152 in Australia’s first innings, having also scored 100 in the hosts’ second Test win in Adelaide.
With Steve Smith also scoring a century in a return to form, Australia put 445 on the board in the first innings and wrapped up India’s reply for 260 in the first hour of day five by capturing the last wicket of Akash Deep for 31.
Australia will have regrets, however, particularly the selectors’ decision to drop Scott Boland for recalled quick Josh Hazlewood, who broke down with a calf injury early on day four and left the hosts short-handed.
Smith may also rue dropping the easiest of catches in the slips to reprieve KL Rahul on the first ball of the same day.