Australia struck an important early blow with the last ball before lunch in the second Test at Perth Saturday, with Mitchell Starc clean-bowling Murali Vijay for a duck.
After Australia's tail collapsed and they were dismissed for 326 on the second day, the left-arm paceman found a gap between Vijay's bat and pad to send his stumps flying.
At lunch, India were six for one, with KL Rahul on one.
India had cleaned up the Australian tail with Ishant Sharma (4-41) on a hat-trick in the second innings.
At 310 for six, the home side were edging towards an imposing first innings total after winning the toss and electing to bat.
But the Indians struck back to claim the last four wickets for just 16 runs on a lively and at times challenging pitch.
Australia resumed at 277 for six, with overnight batsmen Tim Paine and Pat Cummins building a useful lower order partnership.
The pair put on 59 before Cummins (19) was clean bowled by a sharp delivery from Umesh Yadav (2-78) which got through his defences to end his 66-ball knock.
That sparked the Australian collapse, with Paine then trapped lbw by Jasprit Bumrah two balls later for 38.
Sharma claimed the wickets of Starc (6) and Josh Hazlewood (0) in successive balls to end the innings.
Given the nature of the pitch, it seemed a competitive total by the Australians. They will be disappointed, however, that a number of batsmen got starts but failed to make big scores.
Opener Marcus Harris top-scored with 70, with Travis Head adding 58 and Aaron Finch contributing 50, with the latter's 112-run partnership with Harris at the top of the order providing an excellent foundation for the home side.