St. Louis has four goals and 10 points during a five-game point streak. Ryan Malone, Teddy Purcell and Ondrej Palat had the other Tampa Bay (4-2) goals.
Bishop made a strong save in the second on Trevor Lewis' shot from the low left circle. The goalie had missed one game after having his right leg jammed during the third period of last Thursday's game against Florida.
Los Angeles (4-3) goalie Jonathan Quick was pulled late in the second after allowing three goals on 17 shots. Quick had a 3-0 record with an 0.55 goals-against-average in four previous games against Tampa Bay.
Slava Voynov scored for the Kings, who had a three-game winning atreak end. His goal ended Bishop's shutout bid at 10:27 of the third.
St. Louis ended Quick's night on a goal from the low slot that gave the Lightning a 3-0 advantage with 3:38 remaining in the second.
Malone put the Lightning up 1-0 when he re-directed Sami Salo's shot just 19 seconds into the game. Purcell made it 2-0 from the low left circle on Tampa Bay's eighth shot with 7:16 left in the first.
Palat scored late in the third to extend the Lightning lead to 5-1.
Voynov hit the post late in the first for the Kings, who had a goal 32 seconds into the second disallowed because of incidental contact with the goalie. Los Angeles also failed to score during a 4-minute power after Salo received a high-sticking penalty at 3:08 of the second.
NOTES: St. Louis assisted on Malone's goal for his 900th point with the Lightning. Including his time with Calgary, St. Louis has 922 points, which is 94th on the NHL career list. ... Ben Scrivens replaced Quick. ... This was just the fourth time in the last 10 years that the Kings played a road game against Tampa Bay.