India seamer Mohammed Siraj claimed his maiden Test five-wicket haul to dismiss Australia for 294 and set up a close finish on the final day of the series decider at Brisbane.
Siraj made amends for dropping two catches - including Steve Smith, who top-scored for the home side with 55 - as he finished with figures of 5-73 in only his third Test appearance.
Fellow paceman Shardul Thakur also returned Test-best figures of 4-61 to leave the tourists with a victory target of 328, which would be the highest successful run-chase at the Gabba - a venue where Australia remain unbeaten in Tests since 1988.
India openers Rohit Sharma and Shubman Gill faced just 11 deliveries, reaching 4-0 before rain intervened to bring the fourth day's play to a close.
Australia extended their overnight lead of 54 in the morning through openers Marcus Harris (38) and David Warner (48) before losing four wickets in quick succession as they slipped to 123-4.
Siraj picked up two of those in the space of four deliveries, removing the dangerous Marnus Labuschagne (25) before having Matthew Wade caught behind for a duck.
Smith and Cameron Green (37) led the Australian recovery with a partnership of 73, but both were put down by Siraj, who spilled Smith in the deep when he gave off-spinner Washington Sundar the charge.
However, Siraj got his man with a rising ball that struck Smith on the glove and looped into the hands of gully and Green - who had survived a sharp return catch - eventually departed when he edged Thakur to second slip.
Australia captain Tim Paine (27) and Pat Cummins (28 not out) ensured that their side's lead climbed above 300 before Siraj and Thakur cleaned up the tail between them.
It was Thakur who made certain of his team-mate's five-for, taking the catch to remove last man Josh Hazlewood (9) and set up what promises to be an intriguing climax.
Australia must force victory on the final day to regain the Border-Gavaskar Trophy, which will remain with India if the match - and series - ends in a draw.