Paceman Ben Hilfenhaus (4-54) took three wickets in five balls and left Peter Siddle (3-43) to perform the coup de grace on the second ball of the next over by removing Virat Kohli for 75 and leave the tourists all out for 171.
India, bowled out for 161 in the first innings, had resumed on 88 for four still needing 120 runs to match Australia's first effort of 369 and make the hosts bat again.
It was a seventh successive overseas test defeat for India after the 4-0 drubbing they received in England last summer to lose the number one test ranking and questions will be asked about several of their experienced batsmen.
"Class is always there, they have the experience, it's just in back-to-back series that we have failed," Dhoni said in the post match presentation.
"We have not adapted well to the conditions quickly enough. Winning in Adelaide is the only motivation we have now, the bowlers have shown they can take wickets, we need to put more runs on the board."
On a blistering morning at the WACA, which had the fans crowding around the complimentary sunscreen dispensers as they streamed into the ground, India kept the Australians at bay for the first hour.
The quartet of Australian quicks continued to make full use of the bounce on offer from the wicket but, despite several wafted attempted shots from the batsmen, were forced to wait for the breakthrough.
Kohli has been under pressure for his place in the side for much of the series but once again proved to be one of his team's more impressive batsman, bringing up his fifty with a flicked four through long on off Mitchell Starc after an hour's play.
He and Rahul Dravid (47) had put on 84 for the fifth wicket when Ryan Harris finally separated them, fooling the senior partner with a ball that swung in, crashed through the gate and removed the leg stump.
It was the fifth time in six innings in the series that the 39-year-old Dravid, known as "the Wall" for his strong defence, had been bowled.
Mahendra Singh Dhoni came in next but lasted just 20 minutes before edging a Siddle delivery to Ricky Ponting in the slips with the former Australia skipper taking a fine low catch.
With the captain gone India's cause looked lost, not least because their tail has been fragile at best during the series, and so it proved again.
Australia's David Warner was named Man of the Match for his innings of 180, which included the fastest test century by an opening batsman in 69 balls on Friday.
Australia won the first test in Melbourne by 122 runs and the second in Sydney by an innings and 68 runs. The fourth test begins in Adelaide next week.
