Konstantin Pushkarev, Dustin Brown and Jamie Lundmark also scored for Los Angeles, which had dropped seven of its previous eight road games. Frolov, Cammalleri, Sean Avery and Derek Armstrong each had two assists.
The Kings scored six goals on 18 shots through two periods. Panthers goalie Ed Belfour was replaced by Alexander Auld with Florida trailing 3-0 and 5:59 left in the first period.
Florida, which entered the game 6-1-1 in its previous eight home games, was shut out for the seventh time this season.
The Kings began a five-game trip by improving to 7-18 on the road.
Goals by Cammalleri, Pushkarev and Brown gave Los Angeles a 3-0 lead 13:55 into the first period.
Frolov increased the Los Angeles lead to 4-0 when he finished a 3-on-1 by redirecting a centring pass from Avery 3:34 into the second period.
Lundmark and Frolov scored 34 seconds apart to build a 6-0 cushion 14:32 into the second period.
Burke's previous shutout was for Tampa Bay against Pittsburgh on April 8, 2006. He made his sixth appearance since being acquired by Los Angeles on Jan. 18.
Notes: Frolov has 28 goals, including seven in his past eight games. Cammalleri has 22. ... Brown scored his team-high ninth power-play goal. ... Florida defenceman Martin Lojek made his NHL debut by filling in for Mike Van Ryn (hand). Lojek was recalled from Rochester of the American Hockey League on Saturday. ... L.A. hasn't lost at Florida in almost 5½ years, dating back to Oct. 26, 2001. They're 2-0 since then, also winning on Nov. 5, 2003.