"The guys stepped up big. It was a huge effort. It's a big two points," Quick said.
Jose Theodore gave up two goals on 26 shots for Florida, which has dropped three of its last four.
Sean Bergenheim netted the Panthers' only goal, a rebound that cut the deficit to 2-1 with 4:21 remaining in the second period.
Quick stood tall in the third period with 13 saves to help pull out the win.
"We thoroughly outplayed them. ...Their goalie got them a couple of points tonight," said Panthers head coach Kevin Dineen.
Just 1:35 into the game, Johnson wristed a shot from the left circle that bounced off a Panthers defender in front and found its way into the back of the net.
Brown doubled the lead at the 14:13 mark of the second as he took Slava Voynov's two-line pass in stride and lifted the puck top shelf.
Bergenheim had a game-high seven shots...The Panthers have lost seven straight to Los Angeles dating back to November 27, 2002...LA's Mike Richards did not play in the third period due to a possible head injury...The Kings killed off six penalties, upping their streak to 24 straight dating back to November 19.