Australia 273 (Hussey 95, Herath 3-54) and 210 (Clarke 60, Herath 5-79) beat Sri Lanka 105 (Paranavitana 29, Lyon 5-34) and 253 (M Jayawardene 105, Mathews 95, Harris 5-62) by 125 runs
Scorecard and ball-by-ball details

The Michael Clarke era might not match the Ricky Ponting years for sheer victory numbers, but Clarke has at least started his tenure as Australia's full-time Test captain the same way as his predecessor - with a comfortable win over Sri Lanka in Galle. Seven years ago it was Shane Warne who ran through the Sri Lankans in the final innings; here it was Ryan Harris, whose five-wicket haul set up Australia's 125-run win.

The victory was notable for several reasons: as Australia's first Test win on the subcontinent since they visited Bangladesh in 2006, as Clarke's first Test triumph as leader, and as the 100th Test victory in which Ponting has played. Ponting's record is a remarkable one compared to some of his fellow veterans, including Mahela Jayawardene, who with 49 victories has had less than half the team success of Ponting.

Jayawardene was the man who created the most problems for Australia on the fourth day, with his 29th Test century giving Sri Lanka a sliver of hope that they might pull off what would have been a record chase of 379. He and Angelo Mathews combined for a 142-run stand, nearly three times as big as the next best partnership in the match, and showed Clarke that this captaincy caper isn't always smooth sailing.

But Harris broke the partnership by nipping a delivery off the seam and through the tiny gate left by Jayawardene; the ball clipped the inside edge and took his off stump. That was the moment Australia had been waiting for, and with Jayawardene gone for 105, they could finally breathe a sigh of relief.

The only remaining question was whether Mathews, whose highest Test score was 99, would go on to register his maiden century. In the end, as his tail-end partners dwindled away, he lost patience and on 95 tried to bring up triple figures with one shot, but with a swing as wild and woolly as some of the weather in Galle over the past few days, Mathews lost off stump to Shane Watson.

Fittingly, it was Australia's debutant offspinner Nathan Lyon who took the final wicket, having collected five in the first innings. The end came when Suranga Lakmal skied a catch to Johnson, who ran back from mid-on, and the Australians could officially celebrate their proudest moment since the disastrous Ashes campaign last summer.

It was a symbolic victory for the Australians, who had two new players in Lyon and Trent Copeland, a man in his second Test, Usman Khawaja, and a new leader with fresh ideas. It's too early to know whether Australia will climb back up the ICC Test rankings - they need to win the series to jump ahead of Sri Lanka - but at least the tour has started in the best possible way.

For Sri Lanka, there was enough resistance in the second innings for them to wonder what could have been. The difference between the two sides was Sri Lanka's first innings of 105, when too few of their batsmen showed the necessary application on a difficult surface. In the second innings, Jayawardene and Mathews proved that runs were available for those who worked hard.

They balanced solid defence, respecting the good balls, with a run-scoring mindset. Jayawardene lofted a six over long-on from the offspin of Lyon and improvised when possible, including a paddle over his shoulder for another boundary off the offspinner. When he brought up his hundred with a classic late cut, he pumped his fists in celebration; not many of his 29 Test hundreds had come in such trying circumstances.

At the other end, Mathews occasionally threatened to lose his nerve, as when he advanced to Lyon and tried to smash him over long-off, and was lucky that his miscue landed safely in no-man's-land at deep cover. But generally he provided excellent support and he brought up his half-century with a boundary pulled through midwicket off Mitchell Johnson.

The milestone came from his 89th delivery and it gave the selectors some vindication for including him as a specialist batsman, a decision that effectively ruled Ajantha Mendis out of the side. But Sri Lanka's problems were not created at the selection table, they were founded on poor batting from too many of the specialists, particularly in the first innings.

The captain Tillakaratne Dilshan, especially, should be disappointed with himself, as he failed to put a price on his wicket in both innings. In contrast, Australia's captain, Clarke, showed real grit to make 60 in the second innings, and it went a long way to winning the match.

The final day was difficult, but Australia won their hard-earned reward. Like Ponting, Clarke's captaincy career has started with a victory in Galle. Now it's up to Clarke to ensure that, like Ponting's Australians did in 2004, they go on to win the series.

Brydon Coverdale is an assistant editor at ESPNcricinfo