Henrik Samuelsson and Mitchell Moroz each had a goal and an assist for the Oil Kings, who took the second-round matchup in five games 4-1, while Cody Corbett, Reid Petryk and Brett Pollock added the others.
Eric Roy scored the lone goal for the Wheat Kings, who trailed 3-0 after the first 20 minutes of action.
Edmonton's Tristan Jarry made 19 saves for the win as Jordan Papirny turned away 33-of-38 shots for Brandon.
The Oil Kings will face either the Medicine Hat Tigers or the Kootenay Ice for the Eastern Conference championship. The Ice currently lead their series 3-1 and can eliminate the Tigers on Saturday with a win in Medicine Hat.
The Western Conference final is already set as the Kelowna Rockets will square off with the Portland Winterhawks.