It was the sixth successive overseas test defeat for India after their 4-0 drubbing in England last year and put paid to their hopes of a first series triumph in Australia.
Some spirited batting from the tailenders extended the contest beyond the tea break before spinner Ravi Ashwin was caught for 62, a fifth wicket for Ben Hilfenhaus, to end the innings at 400 all out.
India had faced a Herculean task to rescue the match after Australia declared their first innings on 659-4 on Thursday with a mammoth lead of 468 over India's 191.
Sachin Tendulkar's 21st attempt to secure his 100th international century ended when he was dismissed for 80 soon after lunch, triggering a collapse with four wickets tumbling for 15 runs.
Clarke, whose record 329 not out set the hosts on their way to a huge total, made the key breakthrough with his occasional spin-bowling.
Tendulkar resumed on 70 after lunch having reached his 65th test fifty in the morning and had added 10 runs to his tally when he got an edge to a Clarke delivery which deflected off the gloves of wicketkeeper Brad Haddin into the hands of Mike Hussey.
"That's a great win," said Clarke. "I know they made 400 today but that's a really flat wicket out there now and a lot of credit must go to our bowlers on a really tough wicket to take 10 wickets."
Australia took the new ball and Hilfenhaus (5-106) wrought havoc with it, bowling VVS Laxman for 66 with a peach of a ball that just touched the off stump with his first delivery after a rest.
On his next over, the big pacemen had Mahendra Singh Dhoni caught and bowled for two after a review of the television pictures showed the Indian skipper had chipped the ball back to him.
James Pattinson got his first wicket of the innings on the next over, trapping Virat Kohli plumb leg before wicket for nine and leaving India languishing on 286 for seven.
With the match almost certainly lost, Zaheer Khan had some fun with a quickfire 35, which included a huge six, before he was caught by Shaun Marsh off the bowling of Peter Siddle.
Australia won the first test by 122 runs in Melbourne last week.
"It was a good track to bat on, I suppose a few of the batsmen got out on good deliveries but you have to make the most of it," said Dhoni. "I think the Australians really made the most out of it."
