Edmonton improved to 19-5-3 at Rexall Place and their .759 winning percentage on home ice is the best of any team in the Eastern Conference.
Henrik Samuelsson scored twice for the Oil Kings (31-11-5), who regained top spot in the Eastern Conference standings from the Calgary Hitmen, while Dylan Wruck and T.J. Foster each chipped in with two assists.
Trevor Cheek, Edgars Kulda, Curtis Lazar and Stephane Legault scored a goal apiece to round out Edmonton's offence.
Colin Jacobs scored the lone goal for the Cougars (14-26-6), who fell to 5-15-4 on the road.
Laurent Brossoit stopped 20 shots for the win as Brett Zarowny made 36 saves in a losing cause.
Jacobs opened the scoring for the Cougars at 9:21 of the first period on a two-man advantage.
Cheek tied the game up at 13:00 after finishing an easy tap-in from a tic-tac-toe play with Foster and Michael St. Croix.
Lazar put Edmonton ahead on the power play at 2:42 of the second period when he knocked a rebound out of midair past Zarowny, who scrambled to make two initial saves.
Legault tapped in his own rebound while shorthanded at 8:32 to make it 3-1 Oil Kings.
Samuelsson scored twice in the third period and Kulda added one more to blow the game wide open for Edmonton.
The Oil Kings went 1 for 5 on the power play while the Cougars scored once on nine chances with the man advantage.