Australia glimpsed first Test oblivion before a combative stand between Shane Watson and Brad Haddin gave the tourists a chance to press for victory against India on the final day in Bangalore.
Batting again after the Indian tail had reduced the first innings deficit to a mere 70, the Australians struggled to find momentum in the face of withering spells from pacemen Zaheer Khan (1-30) and Ishant Sharma (2-27) and a teasing one from Harbhajan Singh (2-76).
Mike Hussey's dismissal, fooled completely and bowled by Harbhajan's doosra, reduced the visitors to 5-128, a lead of only 198 with no old hands left at the tiller.
But Watson (32no) and Haddin (28no) showed the nerve to counter-attack their way out of a tight spot and when stumps were drawn at 5-193 they had stretched the advantage to 263.
Playing only his fourth Test and first since November 2005, Watson could be well pleased with a day that also featured bowling figures of 3-45, one more wicket than he had managed in his previous three appearances combined.
History will favour the tourists on Monday for the highest fourth innings total in Tests in Bangalore is only 239 - made by India when they lost to Australia in Bangalore in 2004.
There is one injury concern for the Australians, however, with reliable seamer Stuart Clark nursing a sore elbow after being unable to bowl on Sunday morning.
Indian captain Anil Kumble was off the field for more than 90 minutes at the start of the innings while he received treatment for what was thought to be a shoulder problem, but he returned to bowl before the end of play.
Matthew Hayden's ordinary match with the bat concluded when he was lbw for 13, half-forward to a Zaheer inswinger, and Ricky Ponting (17) fought an intriguing duel with Harbhajan.
Ultimately he succumbed to some smart bowling by Sharma, who teased Ponting into flicking a slower ball to short midwicket.
Simon Katich's stolid occupation could have ended on five, when he squeezed a difficult chance to short leg from Harbhajan.
Showing a little more fluency after tea, Katich could have been expected to go on, but the ball after swinging Harbhajan over mid off and the boundary to go to 34, he played back to a top spinner that popped off the wicket and blocked it firm-handed to silly point.
Michael Clarke became the third batsman in this match to ladle a Sharma slower ball to one of the fieldsmen patrolling the cover region.
Hussey (31) had been certainty itself for 523 minutes of batting in this match, but in his 524th he was beaten utterly by Harbhajan.
Shouldering arms, Hussey was helpless as the ball broke back dramatically and rattled the stumps, sending the bowler into fits of delight.
In difficult circumstances, Watson and Haddin proceeded to trust their eyes and their luck, importantly stretching the lead as they did so.
One Watson glance flew through the hands of leg slip, and Haddin slapped a drive through the fingers of Kumble, both shots going for four.
Australian efforts to wrap up the Indian tail in a hurry were earlier delayed for 85 minutes by Zaheer, whose unbeaten 57 took the Indians to 360 in reply to the tourists' 430.
A difficult innings for Haddin was made worse by the fact that his 23 byes, admittedly on a vexing surface for any stumper, were the most conceded by an Australian against India.