Whitney put Phoenix ahead 1-0 on a power-play marker with 7 seconds remaining in the first period, one-timing a feed from Oliver Ekman-Larsson past Jose Theodore.
The Coyotes made it 2-0 midway through the second frame on another power play when Whitney's pass found Radim Vrbata, whose shot trickled past Theodore and into the net.
Mike Smith stopped 19-of-20 shots before leaving with an injury 3 1/2 minutes into the third period. He was replaced by Jason LaBarbera, who stopped all eight shots he saw, including penalty shot by Florida's Stephen Weiss with 25 seconds left.
The win was only the second in six games for Phoenix.
Southeast Division-leading Florida lost for the just the second time in nine contests.
Brian Campbell scored with 2:18 left in the game, but the Panthers could get no closer.
Theodore ended with 20 saves.