Kopitar made it 4-1 at 19:44 of the first period, but Meier scored his fourth of the game at 1:24 of the second period during a power play to make it 5-1.
Meier then pushed the lead to 6-1 with a snap shot at 19:32.
"I can't remember ever seeing a guy that hot," Sharks coach Bob Boughner said. "You put in the good, hard work and you get paid back, and Timo got paid back today. The way he scored, the patience, picking the shot. Those were pretty goals."
Anderson redirected a shot from Drew Doughty at 10:35 of the third period for the 6-2 final.
"Nothing is easy in this game, whether you're fixing or moving forward," Kings coach Todd McLellan said. "So no, it's not an easy fix, but it's addressable. We can be better in those areas, for sure."
Los Angeles outshot San Jose 41-17.
"You could probably summarize this game by looking at the game sheet," McLellan said. "You'd look at the shots on goal and go, 'that shouldn't be like that. But it should be, because one team played on the inside, in and around our paint, and we didn't get inside at the other end."
NOTES:Meier has scored 20 goals in 35 games this season. … Karlsson got his 500th NHL assist on Meier's fifth goal, becoming the fastest active defenseman to reach the milestone (820 games played). Philadelphia Flyers defenseman Keith Yandle did so in 1,033 games. … The last player to score six goals in a game was Darryl Sittler for the Toronto Maple Leafs in an 11-4 win against the Boston Bruins on Feb. 7, 1976.