Captain Griffin Reinhart scored the game winner on the power play at 8:10 of the second period with a cannon from the point that squeezed under the pad of Warriors' goaltender Justin Paulic.
Michael St. Croix, T.J. Foster, Keegan Lowe and Brandon Baddock had the other goals for the Oil Kings (15-5-4).
Tanner Eberle had the lone goal for the Warriors (8-11-6).
Laurent Brossoit stopped 22 shots for the win as Paulic made 35 saves in a losing cause.
St. Croix opened up the scoring on a two-man advantage, rifling home a cross-ice feed from Dylan Wruck.
Eberle put Moose Jaw on the board at 6:07 of the second after he picked up the puck from a deflection off the skate of Edmonton defender Ashton Sautner and tucked in a backhand.
After Reinhart's go-ahead goal, Foster doubled Edmonton's lead at 18:56, fighting off Kendall McFaull to chip the puck over Paulic's right pad.
Lowe gave the Oil Kings a 4-1 lead at 2:38 of the third, jumping on a loose puck in the high slot and wristing it glove-side.
Baddock closed out scoring with a deflection in tight at 13:35.
Edmonton went 2-for-4 on the power play while Moose Jaw failed to score on its only chance with the man advantage.