Clemmensen made 30 straight saves during the second and third periods, allowing the Panthers to seize the advantage with goals from Marcel Goc and Dmitry Kulikov.
Kulikov's tie-breaking score came on a power play midway through the third period and lifted Florida to its fourth victory in five games.
Cory Conacher scored and Craig Anderson made 15 stops for the Senators, who hold the sixth seed in the Eastern Conference despite dropping their fourth straight.
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