Dustin Brown, Rob Blake, Lubomir Visnovsky, Alyn McCauley, Sean Avery and Brian Willsie also scored for the Kings (14-20-5). Ryan Smyth, Daniel Tjarnqvist, Jarret Stoll and Fernando Pisani had the goals for Edmonton. Smyth was back in the Oilers lineup less than a month after suffering a fractured thumb. Despite missing most of December, Smyth still leads the Oilers with 17 goals.
Edmonton (18-16-2) missed a chance to reclaim first place in the Northwest Division standings with the loss.
The Oilers opened the scoring less than five minutes in when their league-best penalty killing unit contributed offensively. Jarret Stoll knocked the puck loose behind the Kings net and it went in front to Pisani, who fired a wrist shot past Los Angeles goalie Barry Brust.
But the Kings countered less than two minutes later on Brown's power-play goal, his 10th of the season. They made it 2-1 five minutes later when Craig Conroy sent the puck to the front of the Oilers net and Willsie tipped it over Edmonton goalie Dwayne Roloson.
The Oilers had a glorious chance to get back into the game with 3:11 to go in the first when Scott Thornton jumped Tjarnqvist and was assessed seven minutes in penalties.
Tjarnqvist scored with just 16 seconds left to play in the first to tie the score 2-2 before Smyth scored early in the second with five seconds left in Thornton's lengthy penalty and Brent Sopel also in the box.
Stoll made it 4-2 for Edmonton just 32 seconds later with another power-play goal.
The Kinds countered with a power-play goal of their own later in the period when Blake scored the first of three second-period goals by the visitors and five straight overall by Los Angeles.
After Frolov tied the score 4-4, Avery put the Kings ahead to stay with 1:59 remaining in the second.
Visnovsky and McCauley, into the empty net, scored for the Kings in the third.
Los Angeles returns to action Friday, playing the second of a three-game road swing in Calgary. The Oilers play host to the Vancouver Canucks on Saturday.
Notes: Thursday's game marked a milestone for Blake, who played in his 700th career game with the Kings.