Jones, the Preds' first-round pick in the 2013 NHL Draft, broke a 1-1 tie on a wrist shot past Carey Price with 1:27 left in the regulation, boosting Nashville to its first road win of the season.
Pekka Rinne stopped 28-of-29 shots for the Predators.
Price ended with 35 saves for the Canadiens, whose four-game winning streak was snapped.
Brendan Gallagher got Montreal's only goal.
Aaron Carter is still in love with Hilary Duff
Ray Liotta sues skin care company over use of likeness