The Kings, one of four teams to hold the top spot in the Pacific Division down the stretch of the NHL season, moved past Dallas into first place with 90 points.
Dallas and Phoenix are tied for seventh and eighth place in the Western Conference with 89 points while San Jose and Colorado are tied for ninth and 10th with 88. Colorado has only two games left to play and the rest of those scrambling for the final playoff positions have four remaining.
Anze Kopitar put the Kings in front just 52 seconds into the game but Jordan Eberle tied it on the power play less than a minute later.
That was all the scoring against Quick, however, and Mike Richards gave Los Angeles the lead for good on a shorthanded goal that came with 9:12 to go in the opening stanza.
Drew Doughty scored on the power play in the second period and Alex Martinez tacked on a goal in the third.
The four goals came against Nikolai Khabibulin, who stopped 28 shots.