Hilfenhaus has already been ruled out of the second Test starting on Boxing Day in Melbourne while Clarke is in doubt.
Sri Lanka had resumed on their overnight score of 2-65.
Siddle made the only breakthrough of the opening session when Michael Clarke completed a brilliant low catch at first slip despite nursing a hamstring injury to dismiss rival captain Mahela Jayawardene for 19.
Kumar Sangakkara was LBW to Shane Watson on 54 but the decision was overturned on appeal. However the star left-hander had no such luck on 63 when Siddle trapped him leg-before and this time the third umpire upheld the original decision.
Sri Lanka were looking safe at tea at 4-186 but Siddle struck in the 98th and 102nd overs to remove Angelo Mathews (19) and Thilan Samaraweera (49).
Starc stepped up in Australia's hour of need to claim the wickets of wicketkeeper Prasanna Jayawardene (21) and tailenders Nuwan Kulasekara (nine) and Rangana Herath (eight) who failed to keep out a yorker at 9-250.
Shaminda Eranga was last man out, caught behind off Starc at 6.04pm (AEDT).
Spinner Nathan Lyon, who was unable to bowl Australia to victory on day five of the Adelaide Test against South Africa last month, had no impact on Tuesday with figures of 0-57 from 32 overs.
- AAP