Montreal had a four-game winning streak snapped.
Rinne has 16 shutouts in his four years with the Predators, having had seven in each of the last two seasons.
Goc scored on a backhander 1:19 into the second and he put a wrist shot past Carey Price with 8:43 remaining in the third. Cal O'Reilly delivered the other Nashville goal 8:55 into the third. Nashville won for the third time in four games.
Price, whose 11 wins this year are second-most in the NHL, stopped 27-of-30 shots.