Ben Walker had the other Royals (9-4-0) goals, while Jared Rathjen made 29 saves for the win.
Alessio Bertaggia scored on a penalty shot for Brandon (6-6-1). Eric Roy and Tim McGauley had goals as well. Goaltender Corbin Boes stopped 28 shots.
The Wheat Kings opened the scoring early in the second period as Bertaggia capitalized on a penalty shot after being tripped up on a breakaway.
Roy added to Brandon's lead on the power play to make it 2-0.
Victoria got on the board in the second with a power-play goal from Walker. His fifth goal of the season pulled the Royals to within one.
Gogolev tied the game for Victoria on a delayed penalty to make it 2-2.
Walker then gave the Royals their first lead of the game, a 3-2 advantage.
Brandon answered back just under a minute later as McGauley squeaked one past Rathjen, sending it to overtime.