At stumps, Phillip Hughes (53 batting) is fighting hard in company of nightwatchman Nathan Lyon (4).
The stage is now set for an engrossing fifth day's play on a deteriorating track as India will try to dismissing seven remaining Aussie batsmen and keep the target within manageable limit with 98 overs permissible.
India lead the series 2-0 after convincing wins in Chennai and Hyderabad, and seemed to be on course to clinch the series despite Peter Siddle's five-for, which helped Australia bowl out the hosts for 499.
Woefully out-of-form prior to this innings, Hughes struck nine fours and a six during his crucial knock. Bhuvneshwar's figures were an impressive three for 25.
The UP seamer had Warner caught behind in the first over, though much of the 'credit' must go to the batsman who played an irresponsible shot to an away-going delivery.
Bhuvneshwar then had Cowan trapped in-front but this time he was a bit lucky as the ball had pitched outside leg and the batsman had made a big stride forward.
There was no doubt as far as his third wicket was concerned as Bhuvneshwar produced a beauty that held its line before knocking over Smith's off-stump.
Resuming on a strong 283 for no loss, India were bundled out for the addition of just 216 runs, as Siddle returned with impressive figures of five for 71.