Brandon Magee got things going for the visitors with a short-handed goal just 30 seconds in, setting the tone for the Royals (6-2), who earned their second consecutive win.
Nathan Burns scored the lone goal for Vancouver (2-5) just 40 seconds into the second.
Victoria went 1-for-3 on the power play, while the Giants struggled with the man advantage, failing to score from five opportunities.
Despite losing, Vancouver outshot the visitors 30-22.
The Royals went into the first intermission with a 1-0 lead following Magee's early effort, before Burns and Carroll exchanged second period goals to bring the score to 2-1 going into the ultimately scoreless third period.
The Giants' Cain Franson missed a penalty shot with under two minutes to play, as Victoria goaltender Patrik Polivka followed him all the way to stop the forward's low, weak shot.
It was a decisive moment from Polivka, who played well throughout, making 29 saves to earn the win. Tyler Fuhr stopped 20 shots.