The Predators, who won two of three games, also had a goal from Steven Stamkos.
Juuse Saros, the goalie for Nashville, recorded 22 saves.
Winnipeg’s two-game winning streak ended when Eric Comrie made 32 saves and Adam Lowry scored.
After returning after a two-week, five-game road trip, Nashville played their first home game and lost 1-2-2.
The Jets were put in a painful situation after the Predators were forced to leave their home at Bridgestone Arena to make room for the CMA Awards.
Stamkos scored during a Nashville power play in the third period. He has three power-play goals in the last three games and has scored six of his seven goals this season with the man-advantage.
Marchessault grabbed a rebound in the slot and beat Comrie with a wrist shot on the glove side just 1:44 after Stamkos’ goal put Nashville ahead 2-1.
Josi scored an empty-netter for his second goal.
This was the second game of the Jets’ season-opening back-to-back.
The Jets play the Minnesota Wild in St. Paul, Minnesota, on Sunday after taking the day off.
After blocking a shot, Jets defenseman Dylan Samberg departed the game in the second period due to a lower-body injury. According to some accounts, Samberg has a broken foot.