Artemi Panarin scored for the Kings (34-26-19), who have won four straight games, tying their longest winning streak of the season (Nov. 9-15). They are 5-0-1 in their past six.
Connor Ingram made 19 saves for the Oilers (40-30-10), who have lost three of four (1-2-1).
Edmonton would have clinched a Stanley Cup Playoff berth with one point. The Oilers can still clinch a berth Saturday if the Winnipeg Jets fail to win in regulation against the Philadelphia Flyers.
Panarin put the Kings up 1-0 at 7:34 of the first period. He stole the puck from Oilers defenseman Evan Bouchard at the blue line in the defensive zone and scored on a breakaway with a wrist shot that beat Ingram to his glove side.
It was Panarin’s 26th point (nine goals, 17 assists) in 23 games since being traded from the New York Rangers on Feb. 4.
Cody Ceci kept Los Angeles in front by diving to knock Curtis Lazar’s shot off the goal line after it trickled past Forsberg at 10:31.
