Mike Green scored the only goal in overtime on the power-play at Verizon Centre to put the Capitals in firm control of this series heading back to Madison Square Garden on Monday.
Green exchanged passes with Mike Ribeiro before firing beyond Henrik Lundqvist eight minutes into overtime.
The Anaheim Ducks enjoyed a 4-0 victory over the Detroit Red Wings to move 2-1 ahead in their series.
They took the lead on a power-play through Nick Bonino late in the second period and dominated the rest of the night, with further goals from Ryan Getzlaf, Emerson Etem, and Matt Beleksey.
Phil Kessel got the decisive goal against his former team early in the third period as the Toronto Maple Leafs beat the Boston Bruins 4-2 to level their series 1-1
Kessel put Toronto 3-1 up after a pair of goals from Joffrey Lupul erased Nathan Horton's early score for Boston.
Johnny Boychuk got one back for the hosts before James van Riemsdyk finished them off.
Jonathan Quick's fifth career play-off shutout led the Los Angeles Kings to a 1-0 victory over the St Louis Blues, trimming their deficit in the series to 2-1.
Quick made 30 saves while Slava Voynov scored in the second period for the defending Stanley Cup champions.