Florida stopped a two-game losing streak overall and a five-game slide on the road in the teams' last game before the all-star break. Washington, limited by several recent injuries on defence, has lost four of its last five games.
The Panthers pressured the Capitals' young defence throughout, coming up with numerous scoring chances and a 42-18 advantage in shots.
Olie Kolzig stopped 38 shots and Dainius Zubrus scored the game's first goal for Washington, but the Panthers took charge after that.
The Panthers turned the game around in the second period, holding an 18-3 edge in shots, scoring twice and taking command.
Washington took advantage of a 5-on-3 power-play when Zubrus beat Florida goalie Ed Belfour from a sharp angle for a 1-0 lead 3:31 into the game.
Gelinas tied it for Florida at 2:42 of the second period. Jozef Stumpel gave the Panthers a 2-1 lead when he scored on a short-handed breakaway at 5:59.
Peltonen added an insurance goal with 8:25 left in the game, and Gelinas sealed the win with an empty-netter in the final minute.
Belfour made 17 saves in the win.
Notes: Washington D Brian Pothier (flu) missed his first game this season. ... Mike Green returned to the Capitals' lineup after missing Thursday's win at Carolina due to a bruised foot. ... Florida C Olli Jokinen is second in the NHL in shots, behind the Capitals' Alex Ovechkin. ... Anthony Stewart also got an assist for Florida, his first point this season.