Australia A need eight more wickets and India A 199 runs on the final day to win their first four-day match in Bengaluru.
The hosts reached 2-63 at stumps on day three after Australia A scored 292 in their second innings to set India A a total of 262 to win.
Victoria duo Chris Tremain (1-16) and Jon Holland (1-34) picked up the wickets of Abhimanyu Easwaran (0) and captain Shreyas Iyer (28), with Mayank Agarwal and Ankit Bawne unbeaten on 25 and six respectively at stumps.
Tremain said Australia's bowlers had their fingers crossed the M. Chinnaswamy Stadium pitch would deteriorate before it was too late to take advantage.
"It might even out a little more. Hopefully for us we can hit a few cracks and get it shooting," he said.
"I think with the weather around and the heat, that will probably be the way it plays out.
"That's what we'll aim for. I'm not sure how India will address it."
In the tourists' second innings, Usman Khawaja and Travis Head resumed on day three at 1-42, a lead of 11 runs.
Head (87) was the star with the bat, forging an 81-run partnership with Khawaja (40) and a 50-run stand with Marnus Labuschagne (37).
Labuschagne fell on the stroke of tea before fast-bowling trio Michael Neser (25), Tremain (25) and Brendan Doggett (17 not out) ensured the Australians secured a lead of more than 250 runs.
Fast bowler Mohammed Siraj took 3-77, while spinners Kuldeep Yadav (2-51) and Krishnappa Gowtham (2-53) also claimed multiple wickets for India A.
"I think it's still evenly poised and we've still got to turn up tomorrow with a full head of hair and give it a really good crack to get a win," Tremaine said.
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