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The start was delayed by 30 minutes due to heavy early morning rain that left wet patches on the outfield.
Australia, who lead the series 1-0, made two changes from the side that drew the second Test in Pallekele earlier this week.
Injured fast bowler Ryan Harris and middle-order batsman Usman Khawaja were left out as former captain Ricky Ponting and seamer Peter Siddle returned to the team.
Sri Lanka, hoping for a series-levelling win in Kumar Sangakkara's 100th Test appearance, axed batsman Thilan Samaraweera, off-spinner Suraj Randiv and leg-spinner Seekkuge Prasanna.
They were replaced by batsman Lahiru Thirumanne, debutant seamer Shaminda Eranga and left-arm spinner Rangana Herath.
Teams
Australia: Michael Clarke (capt), Shane Watson, Phillip Hughes, Ricky Ponting, Michael Hussey, Shaun Marsh, Brad Haddin, Mitchell Johnson, Peter Siddle, Trent Copeland, Nathan Lyon.
Sri Lanka: Tillakaratne Dilshan (capt), Tharanga Paranavitana, Kumar Sangakkara, Mahela Jayawardene, Prasanna Jayawardene, Angelo Mathews, Suranga Lakmal, Chanaka Welegedara, Lahiru Thirumanne, Rangana Herath, Shaminda Eranga.
Umpires: Aleem Dar (PAK) and Tony Hill (NZL)
TV umpire: Richard Kettleborough (ENG)
Match referee: Chris Broad (ENG)
