The visitors started well in the first half before the Indian bowlers struck twice. Ravichandran Ashwin got the first wicket while Shami scalped the second. Usman Khawaja 27(94) and Steven Smith 2(17) were at the crease for the Aussie team at lunch.
The hosts made just one change with Mohammed Shami replacing pacer Mohammad Siraj, who was given rest considering his workload. Australia made no changes to their winning team from the third Test.
The fourth Test between India and Australia will begin on Thursday in Ahmedabad with hosts aiming to book their place in the ICC World Test Championship final with a win.
In a radio interview with NOVA 93.7 Perth ahead of his ongoing visit to India, Albanese confirmed to the hosts, Nat Locke and Shaun Mcmanus, that he and PM Modi will be at the toss for the Ahmedabad Test.
While Australia currently trail India 2-1 and have failed to regain the Border-Gavaskar trophy they so dearly crave, they showed plenty of spirit winning their first Test match on Indian soil since 2017 when they registered a comprehensive nine-wicket triumph over their rivals in Indore.
Dravid said that challenging wickets were a "part of the game" with the talk around pitches raging after the Indore pitch for the third Test received a "poor" rating from ICC.
In a viral video shared by Indian opener Shubman Gill, India captain Rohit Sharma and Virat Kohli were seen celebrating the festival of colours on Tuesday ahead of fourth Test match against Australia.
Kohli has managed just 111 runs from five innings during the ongoing Border-Gavaskar against Australia and will once again come up against the same opposition should India clinch the final spot in the World Test Championship decider with a victory in the fourth Test in Ahmedabad this week.
Steve Smith stood in as captain for Australia after Pat Cummins flew back home after the second Test in Delhi. Cummins will remain at home in Sydney to be at the side of his mother Maria, who is in palliative care due to breast cancer.
Ahead of the fourth Test match against Australia, cricketer Virat Kohli and his wife Anushka Sharma visited the famous Baba Mahakaleshwar Temple situated in Madhya Pradesh's Ujjain district on Saturday.
India and Australia will lock horns in the third Test of the ongoing Border-Gavaskar Trophy at Indore's Holkar Cricket Stadium from March 1 onwards. India are currently 2-0 up in the series, which saw Indian spinners dominating both Tests in Nagpur and Delhi