Matt Halischuk and Gabriel Bourque scored and Shea Weber chipped in with an empty-netter for the Predators, who grabbed sole possession of fourth place in the Western Conference with only their second win six games.
They moved two points in front of the idle Chicago Blackhawks, who they will face in a head-to-head battle Sunday.
Winnipeg, meanwhile, saw its Eastern Conference playoff hopes take a blow with a third loss in four games. The Jets dropped six points behind Buffalo for the eighth and final spot after the Sabres bested Minnesota Saturday.
Tim Stapleton scored and Ondrej Pavelec logged 25 saves for Winnipeg.