St. Louis assisted on Ryan Malone's goal just 19 seconds into the game, which put the Lightning ahead to stay.
He netted his third of the season in the second period, handing the Lightning a 3-0 lead, and added another in the final period as the Bolts won for the fourth time in five games.
Malone, Ondrej Palat and Teddy Purcell each had a goal and a helper in the victory.
Ben Bishop earned the win, stopping 30-of-31 shots.
Slava Voynov netted the only goal for the Kings, whose three-game winning streak was snapped.
Jonathan Quick started in goal for Los Angeles but was pulled in the second period after yielding three goals on 17 shots. Ben Scrivens stopped 6-of-8 shots the rest of the way.