Austin Carroll and Brandon Magee scored for the Royals (16-13-1) while Jamie Crooks added two assists.
Adam Lowry scored for the Broncos (13-16-5).
The first period featured several dangerous chances by the Broncos, including a Lowry shot that rung off the crossbar. Meanwhile, Royals' forward Crooks hit a post at the other end.
Polivka made a number of big saves for Victoria to keep the game scoreless in the first, including several that were right on his doorstep.
Victoria opened the scoring early in the second when Carroll made a move around the Swift Current defense, forced a low shot to the net and then batted in his own rebound.
The Royals made it 2-0 when Magee collected a goal-mouth drop pass from linemate Ben Walker and roofed it behind Broncos' goaltender Eetu Laurikainen.
Lowry, son of Royals' head coach Dave Lowry, put Swift Current on the board late in the third when he snapped a high shot over Polivka's left shoulder.
Laurikainen stopped 28-of-30 shots in the loss.
Victoria went 0 for 4 on the power play while Swift Current went 1 for 2.Suggest a correction