The Panthers prevailed in the 20th round of the tie-breaker, on the 40th attempt across both sides after some stunning clutch goals from the eventual winners.
Florida scored five times when on the brink of defeat in the sudden-death format, as Washington - who went first in the shoot-out - were on target as many times.
But when Alex Ovechkin saw the 39th attempt of the shoot-out saved by Panthers goaltender Roberto Luongo, Nick Bjugstad ended the marathon as Florida claimed a well-earned two points.
The shoot-out easily eclipsed the longest in the major leagues, with the 15-round tie-breaker between the New York Rangers and Washington in November 2005 the previous record.
The Columbus Blue Jackets and Toronto Maple Leafs extended their winning runs in contrasting fashion.
The Blue Jackets made it seven straight successes with a 1-0 shoot-out win over the Detroit Red Wings, with no goals scored in 65 minutes of regulation and overtime.
The Red Wings led the shoot-out after the first round on Pavel Datsyuk's goal but Ryan Johansen made it 1-1 before Boone Jenner struck in the third round as Columbus maintained their winning ways.
Toronto fittingly accrued a sixth consecutive win with a 6-2 triumph over the Anaheim Ducks.
The Maple Leafs have the league's best goals-per-game ratio - they average over 3.5 goals - with Phil Kessel scoring twice and assisting once at the Air Canada Centre.
Kessel assited Tyler Bozak for the game-opening goal on Tuesday - arguably the most important of the contest, as Toronto have won all 14 times in regulation when they have scored first this season.
The Tampa Bay Lightning, the highest-scoring team by one goal to the Maple Leafs, stayed two points clear of Toronto in the Atlantic division standings with a 3-1 victory over the Philadelphia Flyers.
The Lightning came from behind, with Steven Stamkos, Tyler Johnson and Valtteri Filppula scoring for the winners.
The top four sides in the Central division all won, with the Chicago Blackhawks preserving their narrow lead at the top.
The Blackhawks are one point clear of the St Louis Blues, after a 5-3 victory over the Minnesota Wild.
Patrick Kane's powerplay goal broke a 3-3 tie inside the final four minutes, before Ben Smith's empty-netter sealed the points.
Vladimir Tarasenko scored a hat-trick to send the Blues to a 5-2 triumph over the Los Angeles Kings, the winners scoring five unanswered goals from the 13th minute of the second period onwards.
The Nashville Predators were 3-2 shoot-out winners against the Boston Bruins, while the Winnipeg Jets - seven points behind the Blackhawks in fourth - won 5-1 over the Buffalo Sabres.
The Montreal Canadiens are one point behind the Lightning in Atlantic, after running past the Carolina Hurricanes 4-1.
The New York Rangers were 5-2 winners away at the Calgary Flames, while the Arizona Coyotes edged the Edmonton Oilers 2-1 in overtime.