Trevor Lewis, Mike Richards, Alec Martinez and captain Dustin Brown scored for the Kings, who completed their five-game homestand with back-to-back wins after three straight one-goal defeats.
Quick earned his 172nd career victory and surpassed Rogie Vachon. The shutout was the 30th of Quick’s career, two shy of Vachon’s franchise mark.
The Kings recorded their 11th shutout, tying the franchise record set two seasons ago.
Los Angeles scored on three of their first 13 shots against three-time All-Star Roberto Luongo, who finished with 25 saves.
The Panthers, who have lost nine of their past 10 against Los Angeles, played their first game at Staples Center since Dec. 1, 2011.
In other NHL action, it was:
‧ Rangers 2, Devils 0
‧ Canadiens 4, Maple Leafs 3
‧ Hurricanes 3, Jets 2
‧ Flames 8, Oilers 1
‧ Capitals 3, Sharks 2, So