With his teammates playing solid defence in front of him, LaBarbera stopped 17 shots. The Predators were shut out for the second game in a row. They have been outscored 28-9 during the losing streak, their longest since they dropped six straight March 10-21, 2002. They have scored only one goal in three games.
Cammalleri capped the scoring with 1:20 remaining.
Ladislav Nagy, signed as a free agent over the summer, had his first goal for the Kings, at 9:23 of the third, after assisting on two earlier scores.
Cammalleri opened the scoring 6:09 into the game. Lubomir Visnovksy made it 2-0 later in the period.
Raitis Ivanans and Alexander Frolov each scored in the second period to give Los Angeles a 4-0 lead, prompting Nashville coach Barry Trotz to replace goalie Chris Mason with Dan Ellis midway through the period.
Mason faced 19 shots, and the Kings had 17 against Ellis.
Nashville, which tied for the Western Conference lead with 51 victories last season, won its first two games this season before the losing skid started.