Griffin Reinhart, Henrik Samuelsson, Dylan Wruck and Brett Pollock scored for Edmonton (5-2-1), while Cole Benson added two assists.
Miles Koules and Elgin Pearce replied for Medicine Hat (3-4-1). Marek Langhamer stopped 17 shots in taking the loss.
The difference on the night was Edmonton's penalty killing, which held the Tigers to just one goal on nine chances.
The Oil Kings, meanwhile, finished the night 1-for-3 on the power play.