Kulikov forced a 1-1 tie 5 minutes into the middle frame when he unleashed a blast from the left circle that beat Vancouver's Roberto Luongo high to the glove side.
Goc followed 6 minutes later, scoring on a power play during a scrum in front of the net and giving the first-place Panthers their first lead of the game.
Florida outshot the Canucks 14-2 in the decisive second period.
Scott Clemmensen made 25 saves and Florida logged only its third win in 12 games.
Dale Weise scored and Luongo finished with 20 saves for Vancouver, which was coming off a 4-3 victory over Boston Saturday at the start of a four-game road trip.