Dumont, who had two goals Sunday against, scored the opening goal of the game Tuesday in the first period and added a pair in the second to stake the Predators to a 4-2 lead.
Patric Hornqvist accounted for Nashville's other two goals and Pekka Rinne chalked up 32 saves. The Preds have won eight of their last 10 and are in sole possession of second place in the Central Division.
Phoenix got goals late in the first period from Radim Vrbata and Lee Stempniak to tie the score 2-2, but failed to score again despite outshooting Nashville 34-21 for the entire game. Ilya Bryzgalov gave up all five Nashville goals.