Nashville broke a 3-3 tie midway through the third period when Sergei Kostitsyn fed a quick, backhand pass across the crease to Fisher, who was cruising down the left side and redirected it past Ray Emery.
Martin Erat had a goal and an assist for the fifth-seeded Predators, who also got markers from David Legwand and Jordin Tootoo.
Pekka Rinne turned aside 13-of-16 shots as Nashville grabbed the momentum heading into Wednesday's Game 4 of its Western Conference quarterfinal series against fourth-seeded Anaheim.
Teemu Salanne scored twice, giving him four goals in three games, and Matt Beleskey added a marker for the Ducks, who were without suspended winger Bobby Ryan.
Emery made 33 saves.
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