India A still trail by 236 runs heading into the third day, with Shaik Rasheed unbeaten on 36 and Tanush Kotian on six.
Australia A's bowlers kept India A under pressure throughout the innings, with Todd Murphy leading the attack. The Australia spinner finished the day with two wickets for 26 runs from 17 overs, including three maidens.
Sai Sudharsan was Murphy's first victim, departing for eight from 35 balls. Captain Devdutt Padikkal then made 31 before he was bowled by Corey Rocchiccioli.
Yash Rathod was Murphy's second wicket, while Liam Scott dismissed wicketkeeper-batter Kumar Kushagra for 10. Aayush Pandey was the other India A batter to fall, dismissed by Jhye Richardson in the opening over.
Earlier, Australia A had posted 358 in their first innings. Sam Harper top-scored with 128 from 223 balls, including seven fours and three sixes.
India A's bowlers had earlier fought back well, with Anshul Kamboj, Nachiket Bhute and Shams Mulani claiming three wickets apiece.
With India A five wickets down and still 236 runs behind, Rasheed and Kotian will resume the innings on the third morning with the task of closing the sizeable deficit.