Starting on their overnight score of nought, Aussie openers Phillip Hughes (100) and Alex Doolan (91) took the hosts to 202 for no loss after only 50 overs were possible due to rains.
Hughes registered his 26th first-class century with the help of 16 fours and a six, while Doolan managed his 21st first-class fifty, laced with 13 fours and a six.
Medium-pacer Jasprit Bumrah, off-spinner Baba Aparajith and right-arm medium Anureet Singh also went wicketless on a day when the Indian bowlers struggled for line and length.
Manoj Tiwary-led India 'A', though, had its moments during the four-day encounter with the team posting 501 in response to Australia's first innings score of 423.
Wicketkeeper-batsman Naman Ojha struck his third century in as many innings to provide the necessary philip to the batting order. Ojha had scored a double century and a ton in the first and second innings, respectively in the first unofficial Test, which also ended in a draw.
Medium-pacer Chadd Sayers, who shared the new ball with Cutting, also bowled well to bag his sixth five-wicket haul in first-class matches.
India 'A' now head to Darwin for a 50-over quadrangular series, featuring hosts Australia 'A', South Africa 'A' and the National Performance Squad (NPS) of Australia best up-and-coming players.
Brief scores:
Australia A: 423 & 202 for no loss in 50.2 overs (Phillip Hughes 100 not out, Alex Doolan 91 not out).
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