Morgan Klimchuk scored the winner for Regina (21-33-7) at 9:06 of the third, pouncing on a deflected puck to slide it into the open net as the Pats snapped a four-game slide.
Curtis Lazar and TJ Foster had the goals for Edmonton (43-13-5), while Tristan Jarry gave up three goals on just 16 shots in taking the loss.
Lazar opened up scoring for the Oil Kings with his team-leading 33rd goal at 2:03 of the second period, taking a feed from Henrik Samuelsson and roofing it glove side behind Hewitt.
Coming into the contest scoreless in nine power-play chances against Edmonton, the Pats man-advantage clicked just 2:35 later on a point blast from Scheidl through traffic to beat Jarry.
The Regina power play linked up again at 15:43 with a series of crisp passes leaving Scheidl all alone at the side of the net to tap in his second of the night to give the Pats a 2-1 lead.
Foster pulled the Oil Kings even at 5:31 of the third when his point shot deflected off Klimchuk and behind Hewitt.
But Klimchuck would make amends later in the period by picking up the winner for the Pats.
Edmonton's power play, 9-for-14 against Regina heading into the game, was held off the sheet on four opportunities.
The game was the third of four contests between the clubs. In the previous two games, Edmonton had outscored Regina 15-1.