Teenage leg-spinner Piyush Chawla grabbed 5-89 as Australia conceded a 141-run lead against India's second string in a practice match here on Saturday.
The tourists, replying to the Indian Board President's XI total of 455, were bowled out for 314 in their first innings just before tea on the third day of the four-day match.
The game is Australia's final warm-up before the four-Test series opens in Bangalore next Thursday.
Australia, who resumed at 191-4, crashed to 218-9 before last man Stuart Clark proved an unlikely saviour by adding a valuable 96 runs for the 10th wicket with the reliable Mike Hussey.
Left-handed Hussey showed his team-mates the way to tackle spin on Indian wickets with a gritty 126 that contained 14 boundaries and a six.
Clarke, whose batting average from 18 Tests is 11.80, struck four boundaries and two sixes in his defiant 44 before holing out to mid-wicket against home team captain Yuvraj Singh.
Earlier Chawla, 19, and spin partner Pragyan Ojha shared five wickets in the space of 19 runs to slice through Australia's batting.
The tourists added eight runs to their overnight score when left-armer Ojha had Brad Haddin stumped for 34, ending a 71-run stand for the fifth wicket with Hussey.
Ojha dismissed Jason Krejza before Chawla, ignored by the selectors for the first two Tests, gave a stern reminder of his wicket-taking potential.
The leg-spinner quickly added to his two wickets on Friday by removing Brett Lee, Mitchell Johnson and Peter Siddle in the space of five overs.