Smith netted a pair of goals and Cullen contributed a goal with three assists for the Preds, who reeled off a third straight win.
Seth Jones provided Nashville's other goal.
Marek Mazanec stopped 24-of-26 shots to earn the win.
Nazem Kadri and Peter Holland each scored for the Maple Leafs.
Jonathan Bernier made 24 saves.
Notable deaths of 2014 [PHOTOS]