Nashville has won four games in a row while the defending Stanley Cup champion Kings have dropped three of their past four.
Coming off a season-high seven-game road trip, the Predators played their first home game since Jan. 21.
Gabriel Bourque opened the scoring with a goal at 2:54 of the opening period.
From the left corner, David Legwand sent a backhand pass to Bourque in the high slot, and he beat Los Angeles goaltender Jonathan Quick with a one-timer low to the glove side.
The Predators have scored first in seven of their 10 games this season.
Los Angeles outshot Nashville 32-14.
Wilson made it 2-0 at 7:01 of the second period.
Defenseman Kevin Klein carried the puck down the right side and found Wilson skating through the low slot, where he had an easy tap-in for his second goal of the season.
Klein had two assists in the game. He leads all Nashville defenseman with four assists.
Wilson's second goal came at 13:02 of the second.
With Nashville on a power play, Shea Weber fired a slap shot from the center of the blue line. In the low slot, Wilson tipped the shot, and Quick was able to make the save, but Wilson was in front to poke the rebound into the net for his third of the season.
The assist was Weber's first point of the season. Quick finished with 11 saves.
Notes: Los Angeles C Colin Fraser played in his 300th career NHL game. ... Kings LW Dustin Penner was a healthy scratch for the sixth time in the team's past seven games. ... Nashville C Paul Gaustad played in his 500th career NHL game. ... The Predators have been outshot in all but one game this season.