Toronto won five in a row on home ice from Oct. 22 to Nov. 19. The Leafs have just two regulation losses in their past 11 games.
Florida scored twice on their first seven shots of the game to open a 2-0 lead in the first period.
Bjugstad opened the scoring 1:39 into the first, beating Bernier with a backhand blocker side for his 12th goal of the season.
Bergenheim finished off a 2-on-1 feed from Brad Boyes at 13:50 to give the Panthers a two-goal lead. The assist was the 250th of Boyes' career.
It was all Toronto after that as the Leafs scored five unanswered goals.
Franson cut Flordia's lead in half at 16:49 of the first period, beating a screened Clemmensen, and the Leafs scored twice in the first minute of the second period to take a 3-2 lead.
Raymond scored off the rush, with a wrist shot, glove-side on Clemmensen 27 seconds into the second period for his 14th of the season. Van Riemsdyk tipped a Phil Kessel shot past Clemmensen at 57 seconds of the second period, on a power play.
With the goal, van Riemsdyk surpassed his previous single-season goals total of 21 set during the 2010-11 season while he was a member of the Philadelphia Flyers.
Kulemin picked up the insurance marker at 4:00 of the third period, one-timing a Kadri feed, and two minutes later, Kadri set up Lupul for his 16th of the season.
Bozak finished off a 2-on-1 feed from Kessel at 18:37 of the third.
Toronto concludes its three-game home stand Saturday when they host the Ottawa Senators.
Notes: Leafs coach Randy Carlyle expects David Clarkson (elbow) to return during the team's two-game road trip in Florida. … Toronto forward David Bolland (ankle) is 50-50 to return to the lineup prior to the Olympic break according to Carlyle. … Florida forward Shawn Matthias (illness) returned to the lineup Thursday.