Chasing a daunting victory target of 516 after the Indians declared their second innings at 314-3, Australia were reeling at 141-5 at stumps on a benign pitch at the Punjab Cricket Association.
Michael Clarke however defied the Indian attack and was on 42 with six fours at close along with Brad Haddin (37), the duo having put on 83 runs for the sixth-wicket stand.
Off-spinner Harbhajan Singh, 28, started the Australian rot, sending back openers Matthew Hayden (29) and Simon Katich (20) in his sensational opening over before removing Michael Hussey (one) for his 299th Test scalp.
Hayden, who hit Zaheer Khan for two fours in an over, was trapped leg before while Katich lobbed one for Sachin Tendulkar to take a fine tumbling catch at short point.
Ricky Ponting (two) saw his off-stump uprooted by lanky paceman Ishant Sharma who claimed the Australian skipper for the fifth time in as many matches.
Sharma then returned to dismiss Shane Watson (two), who top-scored with 78 in Australia's first innings total of 268, to reduce Australia to 58-5.
Needing 375 more runs with five wickets in hand, the number one side in the world will have to pray for a miracle if they are to stop India from going 1-0 up in the series for the Border-Gavaskar trophy.
The first Test in Bangalore ended in a draw.
History is also against the visitors as the highest successful fourth innings chase is 418 achieved by the West Indies against Australia at St. John's in the 2002-03 series.
The Indians, who made 469 all out in their first outing, declared their second innings an hour before tea to leave Australia four and a half sessions to make the target.
Mahendra Dhoni struck an unbeaten 68 off 84 balls with three fours and one six after Gautam Gambhir (104) and Virender Sehwag (90) added 182 for the opening wicket to consolidate India's lead.
Dhoni, who promoted himself up the order in search of quick runs, completed his 10th Test fifty and also shared a 66-run stand with first innings centurion Sourav Ganguly (37).
Ponting used as many as seven bowlers to check the rampant Indian batsmen who scored at nearly five runs an over, but with little luck.
Gambhir, 27, hit seven fours and a six for his second Test century while Sehwag clobbered eight fours but was unlucky to miss out on a ton on his 30th birthday.
Sehwag offered a thick edge off Peter Siddle (1-62) to Haddin behind the stumps while Gambhir's knock was cut short by White when he had him caught by Michael Hussey at mid-off.
The Mohali Test will be followed by ones in New Delhi (Oct 29-Nov 2) and Nagpur (Nov 6-10).
Highest fourth innings chases in history.
Clarke's wicket my best- Amit Mishra