San Jose Sharks defenceman Kyle McLaren, right, goes flying after a check from Dallas Stars defenceman Philippe Boucher (43) in the second period. (AP Photo/Matt Slocum)
Oleg Saprykin and Yanic Perreault also scored and Mikael Tellqvist earned his first win for the Coyotes, who have won four of five.
Steve Sullivan and Alexander Radulov scored for the Predators, who lost in regulation for just the third time in 23 games (17-3-3) since opening the season with three straight losses.
Ladislav Nagy gained control of a blocked shot low in the right faceoff circle and fed a quick pass in front of the crease to Fisher, who tapped the puck past goalie Chris Mason and into the open left side of the net for his fourth goal.
Mason had allowed long rebounds throughout the game, but the Coyotes were unable to take advantage until late in the second period.