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Nashville has won four games in a row while the defending Stanley Cup champion Kings have dropped three of their past four. Nashville began its streak with a win over the Kings in Los Angeles one week ago.
Coming off a season-high seven-game road trip, the Predators played their first home game since Jan. 21.
"This was a game that I had a lot of concern with," Nashville coach Barry Trotz said. "When you go on long road trips, every coach will tell you there is a fear the first game back."
Rinne stopped eight shots in the first, 20 in the second and just four in the third for the 26th shutout of his career.
"The last few games, I think we have been doing a really good job defensively," Rinne said. "For me, it is way easier for me to control my rebounds, and if I leave a rebound laying around, they are always there for me to save my butt."
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.
"They are a hard-working team," Kings captain Dustin Brown said. "We didn't match their compete in the first, and that was all the difference in the game."
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 defensemen with four assists.
"You've got to work to the inside against them to get anything offensively, on the left side of their ice," Los Angeles coach Darryl Sutter said. "Shea (Weber) plays so much that he's always getting on the ice against (Anze) Kopitar every time, right? That's what he did tonight."
Wilson's second goal came at 13:02 of the second.
With Nashville on a power play, 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 goal of the season.
"I just turned and saw that I had a bit of space," Wilson said. "I knew that it was going to be a fight in front of the net, and the puck just went on my stick. I am grateful for that."
The assist was Weber's first point of the season. Quick finished with 11 saves.
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.
Copyright by STATS LLC and The Associated Press
NASHVILLE, TN - FEBRUARY 7: Gabriel Bourque #57 of the Nashville Predators warms up before the game against the...