The Panthers avoided being swept in their three-game, season-opening swing through Western Canada. They had dropped one-goal meetings with Edmonton and Vancouver to start the campaign.
Vokoun, starting his 13th NHL season and his fourth with the Panthers, made 27 saves. He had a career-best seven shutouts last year.
Dvorak, who did not have a point in Florida's first two games, scored on a wrist shot 4:20 into the contest and then put a slapshot past Miikka Kiprusoff 3:05 later. The other Florida goal came from Shawn Matthias midway through the third period.
Kiprusoff faced only 17 shots.
Florida will play its first home game on Saturday against unbeaten Tampa Bay.
Celebrity Families of 2014 [PHOTOS]