Ryan Harris picked up his second five-wicket haul as Australia beat Sri Lanka by 125 runs in the first Test to take 1-0 lead in the three-match series and give former captain Ricky Ponting his 100th Test victory.
Having to score 379 to win, Sri Lanka faced a much heavier defeat when it lost five wickets for 68 but MahelaJayawardene scored a fighting 105 and shared a gritty 142-run partnership with Angelo Mathews (95) for the sixth wicket to raise their team's hopes.
Jayawardene completed his 29th Test hundred during a 231-ball innings including a six and 15 boundaries. Mathews missed out on his maiden Test century by five runs. He hit eight boundaries off 191 balls.
Harris finished with 5-62. Seamers Shane Watson and Mitchell Johnson took two wickets each.
Ponting is the first player in history to reach 100 Test wins. Australia has the top seven most successful Test players, with Shane Warne (92) and Steve Waugh (86) rounding out the top three.
Sri Lanka's captain TillakaratneDilshan blamed the defeat on his team's dismal first innings batting when it was bowled out for just 105.
"The main cause for this defeat is our poor batting on the second day," Dilshan said. "Even on a bad pitch like this we can't get out for 100 playing seven batsmen.
"If we had scored at least 200 runs (in the first innings) we could have won this match."
Sri Lanka resumed the fourth day on 120-5 and the overnight batsmen carried on with ease, negotiating the morning session without conceding a wicket.
Jayawardene's century came after lunch, putting him level with Don Bradman in the list of most career centuries at number 10. But the Australian great took just 52 matches for 29 hundreds, while Jayawardene needed 120 matches.
Jayawardene's hundred was also the first century scored in the fourth innings by any player at Galle, which traditionally favors the bowlers in the last days of a Test match.
Harris ended the resistance six overs after taking the second new ball when he bowled Jayawardene off the inside edge, leaving Sri Lanka's tail exposed. SurajRandiv could not keep down a riser from Johnson as he edged the ball to captain Michael Clarke at second slip.
Mathews, on 95 and fast running out of partners, tried to hit Watson and was bowled. A Test century again eluded the batsman, who was run out for 99 in a Test match against India.
Australia batted first after winning the toss and made 273 in its first innings. Mike Hussey scored a skillful 95 on a difficult pitch to be named man of the match. Off spinner Nathan Lyon had a dream debut taking a wicket off his first ball and going on to complete a five-wicket haul to help dismiss Sri Lanka for 105 in its first innings.
Australia made 210 in its second innings helped by 60 runs from captain Clarke. Sri Lankan spinner RanganaHerath returned a career-best 5-79.
The second Test match of the series will be played in Pallekele near hill capital Kandy next Thursday.