An unbeaten century from Michael Hussey and a 96-run stand for the last wicket with Stuart Clark saved the Australians the ignominy of having to follow-on against the Board President's XI in India.
However, Ricky Ponting's side remains firmly on the backfoot on the third day of their warm-up match.
Hussey made 126 and was the last man left standing when the Australians were bowled out for 314 runs, leaving them 141 runs behind after the first innings.
By close of play, the President's XI extended the lead to 251, closing the day on 2-110.
Opener Wasim Jaffer was batting four short of a half-century while Yuvraj Singh was on 37.
Piyush Chawla claimed 5-89 from 40 overs and together with left-arm spinner Pragyan Ojha (3- 72), leg-spinner Chawla threatened to bowl out the Australians for far less than the score they eventually achieved.
The Australians had crashed to 9-218, but Clark emerged the unlikely hero, his enterprising knock of 44 helping the Australians crawl over the 300-run mark.
The Australians lost Brad Haddin (34) off the fourth delivery of the day when the wicketkeeper batsman stepped out to hit Ojha only to be stumped by Parthiv Patel.
His dismissal triggered a slide as Jason Krejza (0), Brett Lee (0), Mitchell Johnson (five) and Peter Siddle (two) all fell in a span of just 15 runs.
Clark then walked out to join Hussey and the pair frustrated Yuvraj Singh's side as they batted together for over 40 overs.
Hussey initially shielded Clark from the strike, but the number 11 batsman grew in confidence and soon came into his own.
Clark's knock was studded with four boundaries and a couple of sixes.
Hussey, overnight 54, reached his century in 235 deliveries and in the process embellished his credentials as one of the Australia's most dependable and consistent batsmen.
Clark completed a fine day by getting rid of Akash Chopra (six) quickly in second innings, while Lee got rid of Subramaniam Badrinath (14), the Tamil Nadu player falling prey to poor shot selection.
Yuvraj and Jaffer, however, held firm and walked off holding out the promise of another day of toil for the Australian bowlers on the morrow.
Indian Board President’s XI v Australia
Stumps Day 3
Indian Board President’s XI 1st Innings 455
Australia 1st Innings
Katich c Kohli b Ojha 15
Hayden c Patel b Pathan 20
Ponting b Chawla 41
Hussey not out 126
Clarke lbw b Chawla 18
Haddin St Patel b Ojha 34
Krejza c Yuvraj Singh b Ojha 0
Lee lbw b Chawla 0
Johnson c Chopra b Chawla 5
Siddle lbw b Chawla 2
Clark c Ojha b Yuvraj Singh 44
Extras 9 (b 4, lb 5)
Total 314 (all out; 120.3 overs)
FoW: 1-26 (Hayden, 8.4 ov), 2-54 (Katich, 17.3 ov), 3-94 (Ponting, 30.2 ov), 4-128 (Clarke, 44.1 ov), 5-199 (Haddin, 69.4 ov), 6-203 (Krejza, 71.1 ov), 7-204 (Lee, 72.4 ov), 8-214 (Johnson, 78.4 ov), 9-218 (Siddle, 80.2 ov), 10-314 (Clark, 120.3 ov)
Bowling
Pathan 24-4-80-1
Gony 14-3-47-0
Ojha 34-10-72-3
Chawla 40-7-89-5
Yuvraj Singh 5.3-1-9-1
Sharma 3-0-8-0
Indian Board President’s XI 2nd Innings
Chopra lbw b Clark 6
Jaffer not out 46
Badrinath c Haddin b Lee 14
Yuvraj Singh not out 37
Extras 7 (b 4, nb 3)
Total 110 (2 wickets; 35 overs)
FoW:1-7 (Chopra, 5.2 ov), 2-35 (Badrinath, 12.3 ov)
Bowling
Lee 9-1-30-1 (2nb)
Clark 5-2-10-1 (1nb)
Siddle 7-0-17-0
Johnson 6-1-15-0
Krejza 5-1-13-0
Clarke 3-0-21-0