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.
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