Forsberg took a pretty feed from Ryan Ellis and one-timed it from the left circle past Darcy Kuemper with 6:36 left to put Nashville up 3-2.
It was Kuemper's first-career loss in five starts against the Predators, who have won six of seven and wrapped up a five-game road trip with four wins.
Ryan Johansen added an empty netter for Nashville, and James Neal also had a goal. Pekka Rinne stopped 21 shots for Nashville.
Mikael Granlund and Jason Pominville scored for the Wild. Kuemper, starting in place of regular starter Devan Dubnyk, had 28 saves as Minnesota fell into a first-place tie with Chicago atop the Western Conference.