Having finally bowled their hosts out for 572 in the morning, Michael Clarke's men set about chasing down the 158-run deficit but were unable to build the necessary partnership with Harbhajan and Ravichandran Ashwin in the wickets.
Clarke was unbeaten on 31 at tea and will now shoulder much of the burden in the final session, with the tourists still 64 runs shy of their target after 49 overs of uninterrupted spin and staring a heavy defeat in the face.
Mahendra Singh Dhoni, scorer of an unforgettable double century on day three, was finally out for 224 when he nicked James Pattinson to Matthew Wade. But if Australia thought their work in the field was done, India had other ideas as Bhuvneshwar Kumar and Ishant Sharma added 26 more for the last wicket. Kumar finished with 38 before Peter Siddle wrapped things up.
Australia faced a tough challenge on a pitch that had started to turn plentifully and were given a further obstacle when David Warner was deemed too ill to open. Shane Watson replaced him in his old position and he, along with Ed Cowan, was confronted by spin at both ends from the off.
The ball was doing plenty but Australia looked like they might survive to the break unscathed until Ashwin struck with the final ball of the session, finding the shoulder of Watson's bat and seeing a simple catch swallowed by Virender Sehwag.
That left Australia on 34 for one at lunch, but things failed to improve in the afternoon with Cowan making 32 runs before becoming Ashwin's second victim lbw.
Warner finally came in at number three but within an over partner Phil Hughes was also out without scoring, deceived by a bouncer from Ravindra Jadeja which flew to Sehwag off the batsman's glove.
Warner managed 23 runs but was clearly still feeling the effects of his earlier illness and became India's fourth wicket, trapped leg before by Harbhajan Singh.
And the off-spinner struck again soon after, brushing Wade's (eight) off stump with a straight delivery to leave Australia with a mountain to climb.