Australia set India a modest target of 50 runs to win the first Test in Chennai on Tuesday with almost a full day of play remaining.
Australia had resumed on day five on a turning pitch on 9-232 and were bowled out for 241 – a lead of 49.
No.11 Nathan Lyon was caught at short leg for 11 after adding 66 in 85 minutes for the 10th wicket with allrounder Moises Henriques.
The 26-year-old Henriques capped a fine debut match with an unbeaten 81 after his 68 in the first innings.
Australia had appeared headed for an innings defeat at 9-175, still requiring another 17 runs to make India bat again, before their defiant last-wicket stand.
Indian offspinner Ravi Ashwin claimed 5-95 after his seven-wicket haul in Australia’s first innings.
Spinners Harbhajan Singh (2-55) and Ravindra Jadeja (3-72) were the other wicket-takers with Jadeja getting the breakthrough in the ninth over of the final day.