Hobart: Mitchell Starc claimed five wickets as Sri Lanka were dismissed for 255 runs Tuesday, giving Australia a 137-run win over Sri Lanka in the final session of the first Test.A dogged Sri Lanka had 36 overs to survive after going to tea at 186-4, but lost its remaining six wickets for just 26 runs as Peter Siddle tore through the middle order before Starc claimed a second-innings 5-63. Man-of-the-match Siddle mixed up line and length on the cracked Bellerive Oval pitch to remove Angelo Mathews and Thilan Samaraweera within eight overs of the evening session, leaving Starc to take the last four wickets.Australia's first win in four Tests this southern summer gives it a 1-0 lead in the three-match series. Sri Lanka has now lost nine of 11 tests in Australia. Starc and Siddle, who came close to being the first man to take 10 wickets in a Test at Bellerive Oval, will be Australia's key weapons in the second Test in Melbourne starting Dec. 26.Ben Hilfenhaus joined the long list of injured pacemen during Sri Lanka's first innings, leaving Australia a bowler light for almost the whole match. For much of final day it looked as though Sri Lanka stood a chance of saving the match through the efforts of Kumar Sangakkara, Mahela Jayawardene and Samaraweera.Chasing an unattainable 393 to win after Australia's 450-5 declared and 278-9, Jayawardene and Sangakkara were concerned only with survival and barely looked for scoring shots but still took their career partnership tally to 5,628 runs at an average of 56.28. Already the fourth most prolific partnership in Test history, Sangakkara and Jayawardene resumed on 65-2 and took their third-wicket stand to 65 before the captain edged Siddle to his Australian counterpart Michael Clarke, who seemed untroubled by a right hamstring injury he sustained Monday.It was 144-3 at lunch and Sri Lanka scored just 42 runs from 24 overs in a rain-affected second session for only the loss of Sangakkara, who was trapped lbw by Siddle. Sangakkara successfully referred an earlier lbw decision, but there was no reprieve this time, departing for a 226-ball 63 that means he now averages 57.25 in Australia â where Sri Lanka has never won a test.The draw still looked a strong possibility against a tiring bowling attack, but Mathews needlessly played at a ball outside his off stump and edged through to Matthew Wade. Wade, who earlier handed the wicketkeeping gloves to Phil Hughes while called on to bowl an over just before tea, took the catch to dismiss Mathews for 19 from 61 balls. Wade's over was a maiden.Samaraweera's gritty innings ended in an lbw to Siddle after 49 runs from 140 balls and Sri Lanka's tail was suddenly exposed. Australia pushed all nine fielders into close attacking positions to pressure the inexpert batsmen. Mitchell Starc had Prasanna Jayawardene (21) caught by Mike Hussey, who scored a first-innings 115 not out. Starc then got rid of Nuwan Kulasekara for 9 with an outswinger that nicked through to Wade.That made it 247-8 with Starc bowling to four slips and two gullies and he proceeded to bowl Rangana Herath via his boot for 8 to wrap up the match, finding some extra bounce for an edge from Shaminda Eranga through to Wade. But it wasn't all good news for Australia, with Siddle finding himself at the center of a ball tampering allegation.Sri Lanka team manager Charith Senanayake said the tourists approached match referee Chris Broad to complain about Siddle allegedly lifting the seam on the ball. "It's unofficial, but it's on video and the whole world has seen it so let's see what action they will take," Senanayake said.