Connor McDavid, Darnell Nurse and Mattias Ekholm each had two assists for the Oilers, the No. 2 seed in the Pacific Division.
Stuart Skinner made 25 saves; he was pulled in Game 4 after allowing three goals on 11 shots in the first period.
"I thought it was just huge that we were able to get the win," Skinner said. "The guys in front of me did an outstanding job. Obviously, we were able to score a few goals, which was huge. I think just how we played all night defensively, in the neutral zone, we definitely wanted it tonight.
"Obviously, I've had to go through a lot of experiences to kind of get me to where I am, have the demeanor that you guys (the media) might see. After every single day, tomorrow when we come to the rink, it's another day at work. That just continues. I've got a job to do and I'm going to do my best to do that every day."
RELATED: [Complete Oilers vs. Kings series coverage]
Adrian Kempe had a goal and an assist for the Kings, the No. 3 seed in the Pacific. Joonas Korpisalo allowed four goals on 19 shots before being pulled in the second period. Pheonix Copley made six saves in relief.
"I think we've got to clean up some stuff from tonight," Kempe said. "Our play in our own zone really wasn't good from the start. [We've got to] stay out of the box as much as we can; it's a big factor. They got two tonight on the power play, so it was a big factor as well.
"I think other than that, I think we keep playing aggressive. I haven't really thought about the game too much right now, but we'll go back and look at it tomorrow and see what we can do better."
Evander Kane gave Edmonton a 1-0 lead on a power play at 8:08 of the first period with a wrist shot from the left face-off circle, and Leon Draisaitl made it 2-0 at 10:40, knocking in McDavid's feed from behind the net for his sixth goal of the series.