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It will be Washington's second appearance in the Cup Final; it was swept by the Detroit Red Wings in 1998.
"I'm emotional right now," Capitals captain Alex Ovechkin said. "We've been waiting for this moment for a long time."
Braden Holtby made 29 saves for his second consecutive shutout, Andre Burakovsky scored his first two goals of the Stanley Cup Playoffs, Ovechkin scored his Washington-leading 12th, and Nicklas Backstrom scored for the Capitals.
Holtby has an active shutout streak of 157:13, not including the 2:14 he missed for an extra skater at the end of Game 5. He has made 60 consecutive saves.
"I think our group here really understands what it means to be a team and how to win," Holtby said. "Maybe in the past we've had more skill or were better on paper, but this team, everyone knows their role, everyone pitches in, everyone is comfortable with each other. I haven't been on a team like this where in any situation we're confident in each other, don't get down on each other. It's just a strong group, and that's really hard to come by, something we're going to need to have going forward."