Jones, the Predators' first-round choice in the 2013 NHL draft, got his goal 1 minute into the second period to open the scoring.
The score was tied 2-2 in the early in the final period when Ellis launched a long-range slap shot at the blue line that got past Evgeni Nabokov for the eventual game-winner. Ellis also notched an assist.
Patric Hornqvist added a goal for Nashville, which rebounded from a 4-0 Thursday loss to Toronto.
Pekka Rinne stopped 14-of-16 shots for the Predators.
Nabokov finished with 28 saves.