The pair scored 38 seconds apart early in the final period, breaking a 2-2 tie.
Nyquist's goal proved to the game-winner after Sean Bergenheim drew the Panthers to within one 4:27 into the third with his second goal of the game.
Jonas Gustavsson turned aside 30-of-33 shots, including 10-of-11 in the third, to secure the decision for the Red Wings, who won for third time in four games.
Nick Bjugstad scored and Scott Clemmensen made 27 saves for Florida.
Celebrity Families of 2014 [PHOTOS]