Allen took a quick slap shot from the boards that surprised Carolina goalie Cam Ward on the glove side.
Cory Stillman, Chris Higgins and Dennis Wideman also scored for Florida, which squandered a two-goal lead in the third period before steadying itself for the win.
Scott Clemmensen made 34 saves for the Panthers, who improved to 5-1-2 in their last eight games. Florida also celebrated a rare win at Carolina -- the Panthers are 6-25-2 all-time at the RBC Center.
Zac Dalpe, Zach Boychuk and Jay Harrison had the Hurricanes' goals. Ward made 24 saves but couldn't help Carolina win its fourth straight.
Both teams have played well recently to propel them to the fringes of playoff contention in the Eastern Conference, and both went after each the other in a spirited third period and overtime.
After Stillman gave Florida a 3-1 lead, Carolina rallied thanks to goals from Boychuk and Harrison.
Boychuk scored first when he walked out in front of the net and snapped a shot past Clemmensen's blocker. Harrison scored with a wrist shot from the slot that slipped through Clemmensen's legs.
Earlier in the third period, Stillman, who helped Carolina win the Stanley Cup in 2006, skated down the slot and beat Ward with a quick wrist shot to the blocker side.
Higgins gave the Panthers a 2-1 lead in the second period he planted himself just outside the crease and smacked a rebound of a Dmitry Kulikov shot past Ward.
The teams traded goals late in the first period.
Dalpe, a rookie who was called up from Charlotte on Dec. 31, scored his second goal in two games when he deflected a pass from Troy Bodie, who caught Clemmensen out of the net and centered the puck from behind the goal. The puck went off Dalpe's skate, and the goal withstood a video review.
The Panthers tied the score shortly thereafter when Wideman's shot from the point deflected off a Carolina player and past a screened Ward.