Indian spinner Ravichandran Ashwin grabbed three wickets to restrict Australia to 101 for six at tea on day four as the second Test headed for a thrilling finish in Bangalore.
The visitors started their second innings needing 188 to win but lost skipper Steve Smith for 28 off fast bowler Umesh Yadav, who took two wickets at the M. Chinnaswamy Stadium.
When tea was called Australia needed another 87 to claim victory as the Test hung in the balance.
The visitors started briskly, scoring at over four runs an over, but were soon rattled as Ashwin got into his groove, trapping a dangerous-looking David Warner lbw for 17.
Shaun Marsh became Yadav's first lbw victim as he tried to pad away an in-swinging delivery but was given out.
The batsmen decided not to waste Australia's single remaining review, but TV replays suggested the ball would have missed the off stump by quite a distance.
It was Smith's dismissal that brought the home crowd to its feet, however, as Yadav's delivery stayed low to hit the star batsman's lower pad for lbw.
Drama followed after Smith apparently waited for a signal from the dressing room to seek a referral, something he is not allowed to do, and the on-field umpire quickly ushered him away.
India skipper Virat Kohli was angry at Smith's antics and the umpires were required to cool tempers down.
Earlier Australian pace bowler Josh Hazlewood grabbed six wickets to help bowl out India for 274 before lunch to set up an exciting contest between two top sides.
Australia lead the four-match series 1-0.