Drew Doughty, Anze Kopitar and Viktor Arvidsson also scored to help the Kings improve to 7-0-1 in their past eight games.
Kirill Marchenko scored for Columbus. Daniil Tarasov was pulled in the second period after allowing four goals on 27 shots, and Michael Hutchinson made nine saves in relief. The Blue Jackets have lost five of six.
After dominating the first period but having nothing to show for it, the Kings finally went up early in the second on Doughty’s fifth of the season. He used some nifty stick-handling to get into the slot before tapping in his own rebound.
Kopitar made it 2-0 less than three minutes later, and that was plenty for the Kings to move to a 2-0-1 start on their seven-game homestand.
Copley got his second shutout of the season and third of his career, while taking his record to an unlikely 21-4-3 in 31 appearances. Neither Copley nor Joonas Korpisalo have allowed more than two goals in the seven games since the Kings dealt away franchise icon Jonathan Quick to the Blue Jackets on Feb. 28. A day after going to Columbus, Quick was traded to Vegas.
Since returning from the All-Star break, the Kings are 12-2-2. They have not lost in regulation in nine home games during that stretch, with their lone defeat coming in a shootout against Nashville on Saturday.