In other post-season games, Toronto Maple Leafs beat Boston Bruins and Anaheim Ducks thrash Detroit Red Wings.
NHL play-offs: Washington Capitals edge past New York Rangers
Defenceman Mike Green scored eight minutes into overtime and Braden Holtby turned aside all 24 shots he faced as hosts, the Washington Capitals, claimed a 2-0 advantage in their NHL Eastern Conference first-round series with sixth-seeded New York Rangers.
The third-seeded Capitals, who outshot the Rangers 8-0 in overtime, made the visitors pay after defenceman Ryan McDonagh was whistled for a delay of game penalty.
Mike Ribeiro deked a pair New York players to the ice before setting up Green, whose shot from the high slot sailed past Henrik Lundqvist and inside the right post.
Lundqvist finished with 37 saves for New York, which fell to 1-9 in its last 10 post-season trips to the Verizon Center.
The Rangers, whose lone win was a 4-3 triple-overtime thriller on May 2, 2012, will host Game 3 on Monday.
New York's Rick Nash nearly snapped the scoreless draw with 3:44 remaining in the third period, but his bid on a partial breakaway caromed off the left post.
Washington's Troy Brouwer was whistled for a slashing penalty as Nash unleashed his attempt, but the Rangers failed to record a shot on the ensuing power play.
Lundqvist denied Ribeiro with his right shoulder on a 2-on-1 rush with 5:45 remaining in the second period.
The reigning Vezina Trophy winner was also up to the task midway through the third when he made a brilliant right-pad save on Jason Chimera's one-timer from the doorstep.
Toronto Maple Leafs 4, Boston Bruins 2
Joffrey Lupul scored a pair of goals and James Reimer turned aside 39 shots as visiting Toronto evened their Eastern Conference first-round series at one game apiece.
Phil Kessel scored what proved to be the deciding goal and James van Riemsdyk also tallied as the fifth-seeded Maple Leafs erased a 1-0 deficit with three unanswered goals to rebound from a 4-1 drubbing by No 4 seeds Boston in the series opener.
Game 3 in the best-of-seven series will be played on Monday night in Toronto.
Nathan Horton and defenceman Johnny Boychuk scored goals and Tuukka Rask made 28 saves for the Bruins, who pressed hard for the equaliser until van Riemsdyk converted a rebound for the insurance tally with 3:07 remaining.
Lupul countered Horton's opening goal by scoring twice in a span of just over five and a half minutes in the second period.
He pounced on a rebound of defenceman Jake Gardiner's shot from the point and chipped it into the net at 5:18 before taking a crossing pass from Matt Frattin and tucking a backhander past Rask at 11:56.
Kessel, who has labored to score against the Bruins since he was traded to Toronto, made it 3-1 on a breakaway 53 seconds into the third period.
Boychuk cut the deficit in half with a blast from the point that deflected past Reimer with 9:25 to play.
Anaheim Ducks 4, Detroit Red Wings 0
Jonas Hiller turned aside all 23 shots he faced and captain Ryan Getzlaf collected a short-handed goal and an assist as second-seeded Anaheim won Game 3 of their Western Conference first-round series with hosts Detroit.
Nick Bonino netted his second power-play goal of the series and Matt Beleskey also tallied with the man advantage.
Rookie Emerson Etem scored his first career play-off goal for the Ducks, who claimed a 2-1 lead in the best-of-seven series and will look to push the seventh-seeded Red Wings to the brink of elimination in Game 4 on Monday.
With 4:49 remaining in the second period, Detroit's Justin Abdelkader was assessed a five-minute charging major and a game misconduct after leaving his feet to drill defenceman Toni Lydman.
Anaheim capitalised 18 seconds into the ensuing power play as Corey Perry made a strong move to the net before the puck caromed to Bonino, whose backhander beat Jimmy Howard (25 saves) from the doorstep.
Bonino's goal proved enough for Hiller, who highlighted his third career postseason shutout by making a blocker save on Johan Franzen's bid on a breakaway eight minutes into the first period.
Getzlaf provided insurance 6:33 into the third period with a brilliant individual effort.
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