Australia will set an Adelaide Oval record if they manage to win the first test against India, having been set an imposing target of 323 on day four.
The tourists resumed their second innings at 151-3 on Sunday then enjoyed a productive opening session, underlined by Cheteshwar Pujara's and Ajinkya Rahane's 87-run stand.
Virat Kohli's team were rolled for 307 after losing 73-7 either side of lunch, notably adding a mere 25 runs for their final five wickets.
Nathan Lyon bowled well and grabbed 6-122 but India's prospects of recording their first test win in Australia since 2008, and striking an almighty blow as they hunt a maiden test series win in Australia, remain strong.
The highest successful run chase in a test at the venue is Australia's 315-6, achieved in 1902 against England, while no side has chased down more than 236 since West Indies in 1982.
Australia's batting coach Graeme Hick, speaking before day four started, admitted the pitch is one "where you're never in".
"It's going to be tough ... more than 250 I feel we'd be looking for a couple of heroes," Hick conceded to SEN.
The target would have been even more immense if not for Lyon, who claimed the prized scalps of Kohli and Pujara then was later on a hat-rick when he removed Rahane and Mohammed Shami.
But the offspinner's haul is unlikely to be a source of confidence for Australia's inexperienced batsmen, especially the left-handers, given he was zeroing in on the same rough that counterpart Ravichandran Ashwin will soon delight in.
Pujara backed up his first-innings ton with a knock of 71, remarkably spending 11 hours batting in the low-scoring contest.
Rishabh Pant helped himself to 18 runs off the first over after lunch, delivered by Lyon, but went down swinging to the next delivery he faced from the tweaker.