Josi assisted on Nick Spaling's equalizing goal midway through the first period and added a score of his own in the second for a 3-1 Nashville lead.
Hutton turned aside all 19 shots he faced in the third period as the Predators notched a third win in four games.
Cody Eakin got the only goal for the freefalling Stars, who stumbled to a ninth loss in 10 games.
Kari Lehtonen turned aside 19-of-23 shots.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys