India closed in on a commanding victory in the first Test at Perth Stadium on Monday, claiming two key wickets before lunch on day four. Australia, now at 211 for seven, still need over 276 runs to pull off a near-impossible chase.
Resuming Day 4 on 12-3, the hosts lost Usman Khawaja (four) early after the opener mistimed paceman Mohammed Siraj to wicketkeeper Rishabh Pant.
Harshit Rana bowled with fire, temporarily immobilising Steve Smith with a rib-tickler and getting Travis Head jumping as the pair added 62 to compile Australia's highest partnership of the match.
Siraj had Smith caught behind for 17, bringing more smiles for India, who had been humbled 3-0 in a home test series against New Zealand earlier this month.
With his typical aggression, Head crunched boundaries aplenty through the off-side on his way to 63 not out, bringing up his 17th half-century with a ramp over Pant to the fence.
India were bowled out for 150 on day one before fighting back to skittle Australia for 104. Dual centurions Virat Kohli and Yashasvi Jaiswal then lifted the tourists to 487-6 declared to set a massive fourth-innings target of 534.
Joining Head at the crease is Mitchell Marsh unbeaten on five.
India have won the last four series between the sides.