Australia bowled Sri Lanka out for 253 on day four of the first Test to clinch victory by 125 runs in Galle.
Mahela Jayawardene and Angelo Mathews underpinned a valiant effort by Sri Lanka to save the match after they resumed on a parlous 120-5.
Jayawardene struck a classy 105 and Mathews made 95 but the hosts fell 126 runs short of an improbable victory target of 379.
The Sri Lankan pair could only look on as the rest of their batting line-up collapsed around them to give Michael Clarke his first Test win as captain and Australia a 1-0 lead in the three-match series.
Jayawardene and Mathews had come together on Friday afternoon with Sri Lanka reeling on 68-5 and resumed in defiant mood, batting through the entire morning session in difficult conditions on a dry and crumbling wicket.
But the partnership was eventually brought to an end after lunch when Jayawardene inside-edged Ryan Harris on to his stumps in the seventh over with the second new ball.
Suraj Randiv was yet to open his account when he fell three overs later, fending a Mitchell Johnson delivery into the hands of Clarke at second slip.
Rangana Herath followed soon after having made 12, and Mathews became the ninth wicket when he was bowled attempting to smash Shane Watson out of the ground.
First innings hero Nathan Lyon wrapped things up 10 balls later when he had Suranga Lakmal caught by Mitchell Johnson, although this time the pick of the Aussie bowlers was Harris, who claimed 5-62.