Vegas, which had four points more than Washington this regular season (109-105), has home-ice advantage and will host Game 1 at T-Mobile Arena on Monday (8 p.m. ET; NBC, CBC, SN, TVAS).
"It's going to be a wild ride in Vegas," Washington forward Tom Wilson said. "That's going to be a heck of a show and we're looking forward to a pretty historic final here."
It's the second time the Capitals have advanced to the Stanley Cup Final. They were swept by the Detroit Red Wings in 1998.
The Capitals lost the two games to the Golden Knights this season, 3-0 on the road Dec. 23 and 4-3 at home Feb. 4. Matt Niskanen, Nicklas Backstrom and Chandler Stephenson scored for Washington, and Braden Holtby (3.00 GAA, .893 save percentage) and Philipp Grubauer (4.10 GAA, .871 save percentage) each started one game.
Reilly Smith and Alex Tuch each had two goals and an assist, and Marchessault had three assists for the Golden Knights. Marc-Andre Fleury had a .939 save percentage and one shutout winning the two games.
"Obviously their goalie's playing great and they work together," Washington defenseman John Carlson said of Vegas. "They work together really well and kind of attack you with five guys. Kind of like the last three teams we faced. It's going to be a tall task, but I have confidence and faith in this group and what we're capable of."
The Golden Knights are the third team to advance to the Stanley Cup Final in their inaugural NHL season, joining the Toronto Arenas (1918) and St. Louis Blues (1968). Vegas is the sixth team to reach the Cup Final in its first postseason appearance, joining the Arenas, Blues, Montreal Maroons (1926), Boston Bruins (1927) and Florida Panthers (1996).
Vegas defeated the Los Angeles Kings in four games and the San Jose Sharks in six games before eliminating Winnipeg.