Vanek, 34, was acquired by the Blue Jackets in a trade with the Vancouver Canucks on Monday. He had 41 points (17 goals, 24 assists) in 61 games with the Canucks.
Columbus, 3-1-0 in its past four games after going 2-6-2 in its previous 10 games, holds the second wild card into the Stanley Cup Playoffs from the Eastern Conference, five points ahead of the Carolina Hurricanes, and trails the Pittsburgh Penguins by seven points for third place in the Metropolitan Division.
The Kings, who seek their third straight win and are 5-2-0 in their past seven games, are in third place in the Pacific Division, two points behind the San Jose Sharks and one point ahead of the Anaheim Ducks.