Antti Niemi was touched for both goals on 33 shots for the Sharks, who have lost their past two games.
At the 8:37 mark of the first, the Kings took a 1-0 lead when Moreau fired the puck on net from a sharp angle at the right side.
Richards made it a 2-0 game when he slammed home a Simon Gagne feed in front of the net at the 4:16 mark of the second.
The Kings appeared to take a 3-0 lead six minutes into the third when the puck found its way into the net with Slava Voynov and Dustin Brown hovering around the net. It was initially called a goal, but replay showed that Voynov kicked it in.
It didn't matter, though, as Quick stopped 13 shots in the third to post the shutout.
Los Angeles hosts Florida on Thursday...San Jose welcomes Montreal on Thursday...San Jose won the previous meeting between these two clubs, a 4-2 decision in San Jose on Nov. 7. The next times these clubs meet will be on Dec. 23 in Los Angeles...Quick has 18 shutouts in his career.