Nashville let a 3-1 lead get away by giving up four goals in the second period, and then staged its own comeback to snap Vancouver's five-game winning streak.
Five of the game's 11 goals came on the power play and the teams combined to score six times in the middle period. Fisher's third-period goal, his second of the game, was the only score in the stanza.
David Legwand, Fisher and Shea Weber all scored in the first period for the Predators, who took a two-goal cushion into the second. Vancouver then stormed from behind on unanswered goals by Daniel Sedin, Aaron Volpatti, Alex Burrows and Jannik Hansen in a span of 7:19 of the second.
Both sides made goaltending changes in the high-scoring affair.
After giving up five goals on 24 shots, Nashville's Pekka Rinne was replaced by Anders Lindback, who stopped all 19 shots he saw while Nashville was staging its rally.
Cory Schneider was given the start for the Canucks and he allowed three goals on just five shots. Roberto Luongo came on and gave up the last three goals on 15 shots to take the loss.