Gregory Campbell also scored and Ed Belfour made 30 saves for the Panthers, who have won five straight.
Jakub Klepis and Chris Clark scored goals for the Capitals, who have lost four of five. Brent Johnson stopped 32 shots, but Washington lost to Florida in overtime for the first time.
During a power play in overtime, Stephen Weiss shot from the right circle and the puck hit Gelinas and went in at 2:01 to win it for Florida.