Florida remains a point ahead of Washington, which defeated the Islanders on Tuesday, for the top spot in the Southeast Division and third overall in the Eastern Conference. Florida is four points back of Boston -- which lost in Tampa -- for second in the conference.
Tyler Bozak and Mikhail Grabovski both scored for the Maple Leafs, who have dropped five straight. James Reimer gave up four goals on 26 shots in the loss.
Toronto's playoff hopes are quickly fading as the team remains 10 points back of Washington for the final playoff spot with just 12 games to play.
Florida took a 1-0 lead just 59 seconds into the game after Bergenheim jammed home a rebound in front of the net.
The score remained that way until the 14:43 mark of the second period when Goc sent a pass from the top of the right circle to the slot where Garrison redirected the puck past Reimer.
Toronto got one back with 58 seconds to play in the second as Bozak tipped in a Clark MacArthur pass to make it a 2-1 game.
Florida, though, scored on a pair of power plays as Kopecky struck 6:07 into the third on a slap shot and Goc's ninth of the season just over four minutes later made it a three-goal game.
Grabovski cut the deficit to two with 6:10 to play, but that was as close as it got as Bergenheim scored into the empty net with 1:20 to play.
Florida hosts Boston on Thursday...Toronto plays in Tampa Bay in the third game of a five-game road trip on Thursday...Florida won all four games in the season series with Toronto...Florida went 2-for-4 on the power play while Toronto was 0-for-2.