At the close of play, India, needing to win to have any hope of retaining the Border-Gavaskar Trophy, were 88-4 in their second innings after yet another collapse, an overall deficit of 120 runs.
Veteran Rahul Dravid was unbeaten on 32, with Virat Kohli on 21. Australia were dismissed earlier for 369 in their first innings, bolstered by a pugnacious 180 from opener David Warner, giving the home side an overall lead of 208 after the Indians made just 161 in their first innings.
Paceman Umesh Yadav picked up his first five-wicket Test haul in the Australian innings to give the tourists some hope, but their ageing top-order batsmen again failed to deliver in India's second innings.
As was the case in their 122-run defeat in Melbourne and innings loss in Sydney, the Indian rot set in early in their second innings. Young left-arm paceman Mitchell Starc picked up the wicket of opener Gautam Gambhir (14), caught in the slips from a steepling delivery in his first over.
Out-of-form opener Virender Sehwag never looked comfortable and fell to Peter Siddle one run later for 10, while Sachin Tendulkar will have to wait at least one more Test for his 100th international century, after being trapped leg-before wicket by Starc for a paltry eight.
Tendulkar, the greatest batsman of modern cricket, arrived and left to a standing ovation from a sellout crowd that probably saw him in action for the last time in Perth.
Starc said he cherished the moment when he dismissed the Indian great.
"It's an amazing feeling. Any time you take a test wicket it's special," Starc said. "To get the 'Little Master,' it was great feeling. ... We have been good with our plans and being strict on ourselves has helped. Hope we can continue with that into tomorrow."
However, three wickets fell to Yadav before lunch - Cowan (74), Shaun Marsh (11) and Ricky Ponting (seven) - sparking an Indian fightback. Warner, dropped on 126, looked set to become the second Australian batsman to pass 200 in as many innings, but he holed out to a back-pedalling Yadav at long-on off paceman Ishant Sharma.
Yadav completed the catch inside the boundary rope, ending a remarkable 159-ball knock by Warner. His innings featured 20 fours and five sixes, the opener raising his century off just 69 balls - the equal fourth-fastest in Test cricket - late on the first day.
"I am very happy with my performance but at the same time we're going to lose this Test match," Yadav said of his maiden five-wicket haul in only his fifth Test match. "What I learned from the Australian bowlers is to bowl a good line. I think that helped me."
Yadav, who caught Warner in the outfield, said he felt a lot of pressure when taking the catch.
"The batsman was on 180 and if I had dropped [it] the situation would have been worse for India," Yadav said.
Skipper Michael Clarke, who scored an unconquered 329 in the second Sydney Test, went for 18, caught behind off Zaheer Khan. Khan had the last laugh in his personal war of words with Brad Haddin, having the wicketkeeper caught behind for a three-ball duck.