Ben Hilfenhaus ripped through the top order to leave India on 55-4 in pursuit of 216 for victory at stumps on day four of the opening Test in Mohali.
Hilfenhaus removed Gautam Gambhir, Virender Sehwag and Suresh Raina during a superb spell of new-ball bowling.
Doug Bollinger also chipped in with the wicket of Rahul Dravid, caught behind, as India wasted the earlier good work of their bowlers.
Australia had also struggled with the bat, crumbling from 87-0 to 192 all out in their second innings shortly after tea - seamers Ishant Sharma (3-34) and Zaheer Khan sharing six wickets.
Zaheer's haul of 3-43 saw him become the second Indian seamer, after Kapil Dev, to reach 250 Test wickets.
Australia had looked in good shape during the early exchanges on the fourth morning as opening batsman Shane Watson, fresh from his 126 in the first innings, blazed a half-century from 51 balls.
But his dismissal, chopping an Ishant delivery onto his stumps, was the start of a collapse to 100-3 at lunch.
Ishant removed Ricky Ponting (4) later in the same over as Australia's skipper, having punched his first ball through the covers for four, pulled straight to backward square-leg.
Michael Clarke almost became the third victim of the over, flicking his first delivery to midwicket and starting to walk off before umpire Billy Bowden decided to check if it was a no-ball with the third umpire - it was, and Clarke survived.
But not for long as, in Ishant's next over, Clarke (4) could only fend a vicious lifter to Mahendra Singh Dhoni behind the stumps.
The tourists' meltdown continued in the afternoon - opener Simon Katich had been at his obdurate best, taking 118 balls to reach 37 before left-arm spinner Pragyan Ojha (2-59) induced a thin edge through to Dhoni shortly after changing his angle to around-the-wicket.
The runs had dried up by this stage and India kept making inroads, Mike Hussey next to go, lbw to off-spinner Harbhajan Singh (2-40) having battled his way to 28.
And Marcus North (10) soon followed, also to Harbhajan, on the stroke of tea, caught via bat and pad by substitute fielder Cheteshwar Pujara at short-leg to reduce Australia to 165-6.
Pujara picked up another catch in the first over of the evening session, Tim Paine offering a sharp chance to silly point off the full face of the bat as he pushed forward to Ojha.
Zaheer then took centre stage, reverse swinging through the lower order - Mitchell Johnson (3), Nathan Hauritz (9) and Hilfenhaus (6) - to finish with figures of 3-43 and join Anil Kumble, Kapil, Harbhajan and Bishan Bedi in India's 250-wicket club.
Hilfenhaus, however, put the game firmly back in the melting pot by taking 3-22 from seven overs at the start of India's run chase.
The Tasmanian seamer won a questionable lbw decision from Bowden against Gautam Gambhir (0) in the first over to set the tone - Gambhir left to rue the lack of the umpire decision review system in this series.
And, after Bollinger (1-17) tempted Dravid (13) into playing too far outside his off-stump at the other end, he had Sehwag (17) caught in gully by Hussey and Raina (0) held in the same region by North.
Sachin Tendulkar (10no) and nightwatchman Zaheer (0no) will resume on the final morning with a further 161 required to complete what would by the fourth highest run chase ever on Indian soil.