Speedster Aaron, who took three for 41, came up with timely blows before off-spinner Yadav struck thrice towards the end to bowl out Australia for 228 in their first innings at 228.
India were 44 for two when bad light led to stumps on day two with openers Faiz Fazal (6) and Akhil Herwadkar (23) back in the hut They were bowled out for 230 in their first innings on Day 1.
Earlier, Australia collapsed to 228 all out as they suffered a batting collapse after being comfortably placed on 157 for two at one stage with opener Joe Burns (78) and captain Peter Handscomb (87) stitching an 118-run stand.
Burns ended up with 11 fours and a six while his skipper smashed 14 fours along with a maximum. However, their dismissals turned things around drastically with the fall of Burns and later Handscomb, who was run out by Herwadkar.
The Indian pacers made inroads into the opposition line-up before spinner Yadav cleaned up the tail.
While Aaron and Yadav were the standout bowlers, handy contributions came from Hardik Pandya (2/33) and Shardul Thakur (1/45).
Brief scores:
India 'A': 230 and 44-2 in 12 overs.
Australia 'A': 228 (Burns 78, Handscomb 87; Aaron 3-41, Yadav 3-44).
Image: Fast bowler Varun Aaron
Photograph: Getty Images