Australia were batting India out of the opening cricket Test on the third day and had extended their lead to 395 runs at the Melbourne Cricket Ground.
The Australians built on their 147-run first innings lead to be 248 for five at tea with Michael Clarke raising his sixth half-century on 52 and Adam Gilchrist not out one.
Only three teams in Test cricket history have scored 400 or more runs in the fourth innings for victory.
The West Indies scored a Test record 418 for 7 to beat Australia at St. Johns in 2003, India amassed 406 for 4 to down the West Indies in Port-of-Spain in 1976 and Australia hit 404 for 3 to defeat England at Headingley in 1948.
The highest successful run chase in the fourth innings at the MCG is England's 332 for seven established 79 years ago.
But the drop-in pitch at the MCG is playing low and high scoring will be problematic in the fourth innings as temperatures are expected to rise over the remaining days of the Boxing Day Test.
The Australians lost five wickets during Friday's two sessions of play.
Before lunch the Indians claimed the wickets of first-innings centurion Matthew Hayden and skipper Ricky Ponting and followed up with the dismissals of Phil Jaques, Mike Hussey and Andrew Symonds.
Opener Jaques picked up his sixth consecutive Test half-century and was out next ball to a return catch by Anil Kumble for 51 shortly after lunch.
Hussey wrestled for 36 off 84 balls with no boundaries before he was caught by Sachin Tendulkar at first slip off RP Singh.
Symonds had an eventful innings, bowled off a no-ball by Zaheer Khan when on six and then clouted both spinners Kumble and Harbhajan Singh for sixes before he was leg before wicket to Zaheer Khan for 44.
Harbhajan picked up the wickets of Hayden and Ponting in four balls in the only road hump in Australia's steady accumulation of runs in the morning session.
Hayden had just past 8,000 Test runs when he skied finger-spinner Harbhajan off a leading edge to Sourav Ganguly at long-off for 47.
The first-innings centurion batted for 84 minutes and hit six boundaries off 54 balls.
Ponting failed for the second time in the Boxing Day Test when he was caught at slip by Rahul Dravid playing forward for three in Harbhajan's next over.
His four and three were his first single digit scores in a Test since six and a duck against India at Calcutta 72 Tests ago in March 2001.
Harbhajan, who went wicketless and conceded 61 runs off 20 overs in the first innings, claimed his 250th Test wicket with Ponting's dismissal in his 61st Test match.
Harbhajan's Test career high point was his 32 wickets at 17.03 in the three-match home series against Australia in 2001.
Overall Harbhajan has taken 58 wickets against Australia.