With the Preds clinging to a 2-1 lead, Wilson got control of the puck along the left halfboards in the Stars' zone, stickhandled into the crease and unleashed a backhander that got past Kari Lehtonen with 4 minutes left in the frame.
Nashville would need the tally when Alex Goligoski scored for Dallas late in the third period to make it a one-goal contest.
Shea Weber and Gabriel Bourque also scored for Nashville, which won for only the second time in six games.
Pekka Rinne earned the victory with 22 saves and also assisted on Wilson's goal.
Michael Ryder added a score for Dallas and Lehtonen managed 18 saves as the struggling Stars lost for the fifth time in six contests.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys