New York moved in front in the Eastern Conference semifinals 2-1 and will take on the Capitals Saturday in Game 4 in Washington.
In the longest playoff game this year, Dan Girardi collected the puck behind the Washington net and fired a pass in front to Gaborik. His wrist shot beat Braden Holtby and prevented New York from tying a dubious NHL record.
New York had lost seven consecutive playoff games decided in overtime, one off the league mark shared by Philadelphia and Calgary.
Ryan Callahan gave New York the lead with a power-play goal 6:41 into the second period. John Carlston tied it less than 5 minutes later and the game then turned into a marathon duel between Holtby and New York's Henrik Lundqvist.
The goaltenders combined for 92 saves -- 47 of them by Holtby.