Ben Walker added two goals for the Royals (13-12-0).
Raymond Grewal and Jarrett Fontaine scored for the Cougars (9-12-4).
Patrik Polivka made 31 saves for the win as Brett Zarowny stopped 25 shots in a losing cause.
Victoria failed to score on its only chance with the man advantage while Prince George went 1-for-6 on the power play.
Grewal opened the scoring 6:20 into the first period on a quick one-timer from the slot while on the power play.
Walker spun around at the hash marks and slid a low one past Zarowny to tie the game just over four minutes later.
The Royals took a 2-1 lead when Walker converted a dangerous three-on-two rush for his second goal of the period.
The Cougars evened the game at 2-2 on a goal-mouth scramble that was finished off by Fontaine.
Cote scored the winner on a low point shot through a mess of bodies to give the Royals the victory in the second night of a doubleheader. Victoria and Prince George split the back-to-back games.