Washington also claimed an Eastern Conference playoff berth after Buffalo, who lost 2-1 to Philadelphia, were eliminated from contention.
Washington, who made the playoffs for a fifth consecutive season, came into Thursday's game deadlocked with Buffalo on 88 points for the East's final playoff spot, but can still win the Southeast if Florida lose in regulation and the Caps beat the New York Rangers on Saturday.
The Capitals raced to a 3-0 lead on goals from Jay Beagle, Alex Ovechkin and Brooks Laich before Florida fought their way back with strikes from Mikael Samuelsson and Ed Jovanovski.
Alexander Semin iced the win for Washington late in the third period.
It was not all good news for the Capitals, however, after netminder Michal Neuvirth left the game in the second period with a left leg injury.
In Philadelphia, Matt Read ended Buffalo's playoff hopes on a breakaway goal with 4:21 left in the third to break a 1-1 tie.
Ville Leino score the Sabres' goal in the second period before Marc-Andre Bourdon tied the score at 1-1.
Ryan Miller had 33 saves for Buffalo.
Also in the East, the Pittsburgh Penguins sealed the conference's number four seed with a 5-2 win over the Rangers.
(Reporting by Gene Cherry in Salvo, North Carolina)