Doughty rear-guard action by the Australians took the first cricket Test into the fifth day with the visitors leading India by 40 runs with a wicket in hand at the end of the fourth day in Chennai on Monday.
Australia were 232 for nine in their second innings, largely due to an unbeaten 75 by Moises Henriques. He was joined at the crease by Nathan Lyon (8).
Ravichandran Ashwin took five Australian second innings wickets for India.
Earlier Monday, India were all out for 572, in reply to Australia's first innings score of 380.