Rahul was an unbeaten on 48, helping India recover from the early loss of Abhinav Mukund, who was picked at the last minute in place of an injured Murali Vijay.
The players walked off for lunch after off-spinner Nathan Lyon's dismissal of Cheteshwar Pujara in the 28th over at the M Chinnaswamy Stadium.
Coming off a humiliating defeat in Pune, India trail the four-match series 0-1.
Pace spearhead Mitchell Starc was the one who gave the visitors the initial breakthrough, as he trapped the batsman who figured in the playing XI after a gap of five and a half years.
Rahul and Pujara (17) added 61 runs in 25 overs to steady the innings.
However, Lyon sent back Pujara when he got an inside edge and the ball lobbed up for Peter Handscomb to complete a catch at forward short-leg, tilting the scales slightly in favour of Australia after the first session's play.
Rahul faced 93 balls and struck eight boundaries during his stay in the middle.
Earlier, India skipper Virat Kohli won the toss and elected to bat.
Australia have named an unchanged XI, while India have brought in Mukund and Karun Nair. Mukund is making a comeback to the Test side after five and a half years, replacing Vijay, who suffered a last-minute shoulder injury.
Nair, who had scored a triple century in his last Test, also got a chance after India decided to drop Jayant Yadav for an extra batsman.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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