Evgeni Dadonov also scored and Michal Repik had two assists for Florida (3-3).
Clemmensen, signed as a free agent in the offseason as the backup to Tomas Vokoun, smothered a point-blank shot by Dallas rookie Jamie Benn 25 seconds into the final period.
Benn ended Clemmensen's shutout bid at 10:11 of the third period while the Stars (2-2) skated 5-on-3.
Climie, who stopped 12 of 13 shots, was beaten by Wilson from the left circle at 11:09 of the second period. At that point, Climie was replaced by Krahn.