Australia dismissed India for 169 in their second innings to secure an impressive 122-run victory on day four of the first Test in Melbourne.
With India needing 292 to win, pacemen James Pattinson (4-53), Ben Hilfenhaus (2-39) and Peter Siddle (3-42) took five wickets between them after lunch to leave the tourists 117-6 at tea.
Spinner Nathan Lyon took the final wicket to clinch the victory.
Earlier, Mike Hussey was finally out for 89 in Australia's 240.
That left India needed to achieve the fourth-highest winning total at the Melbourne Cricket Ground if they were to secure victory in the first of four Tests.
But Hilfenhaus removed Virender Sehwag before lunch and India then collapsed in the second session, with Gautam Gambhir and Rahul Dravid failing to make an impact.
Sachin Tendulkar, still chasing a 100th international hundred, looked to settle his side but was dismissed for 32 when Siddle, with the first ball of his second spell, had him caught in the gully.
"It's a great start to the series," Australia captain Michael Clarke said at the presentation ceremony. "India are a fantastic team and it's great to get a win up but we know they'll come back hard at us in (the second Test at) Sydney."
"You have to give credit to the Australian bowling attack because they bowled really well," said India captain Mahendra Dhoni. "We are known to be tentative starters and I think in the next game it will be slightly better."
AUSTRALIA V INDIA
26-30 Dec: 1st Test, Melbourne
3-7 Jan: 2nd Test, Sydney
13-17 Jan: 3rd Test, Perth
24-28 Jan: 4th Test, Adelaide
1 & 3 Feb: 2x Twenty20
5 Feb-2 Mar: Triangular one-day series- Australia, India, Sri Lanka