India A will need to score another 199 runs on the final day in their pursuit of a tricky target of 262 against Australia A in the first 'Test' of the two-match series.
A stumps on the third day, India A were 63 for 2 with in-form Mayank Agarwal batting on 25 in company of Ankit Bawne (6 batting).
Abhimanyu Easwaran (0) and captain Shreyas Iyer (28) left the scene, leaving India A struggling at 33 for 2 in 9.1 overs.
Earlier, Travis Head's crucial 87 helped Australia A reach 292 after bveing reduced to 134 for 4 at one point.
Batting first, Australia A had scored 243 in the first innings with the help of an unbeaten century by Usman Khawaja, but his performance was overshadowed by pacer Mohammed Siraj's 8 for 59.
In reply, India took a slender lead of 31 runs over Australia A before posting 274 all out in first innings, with the help of Bawne's patient 91 runs.
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Michale Neser (4 for 61) and Jon Holland (3 for 89) were the most successful bowlers for Australia A as they picked up seven wickets between them.
Resuming day three at 42 for 1, Head scored a fighting 87 off 162 balls with 13 boundaries, as he revived Australia A innings after they lost three quick wickets including Khawaja and Mitchell Marsh, who unfortunately was run out for nine.
He brought respectability to the Australia A total before he was cleaned up by Krishnappa Gowtham.
While Head's dismissal left Australia A at a difficult 184 for 5, the tail wagged considerably as Marnus Labuschagne (37), Michael Neser (25) and Chris Tremain (25) - made useful contributions taking the lead past 250-run mark.
The star bowler for India A was once again Siraj, who picked three wickets for 77, taking his match tally to 11 wickets.
Spinners Gowtham and Kuldeep Yadav bagged two wickets each and Navdeep Saini claimed one.