The Penguins will seek their second consecutive trip to the Stanley Cup finals when they take on either Carolina or Boston for the conference title.
The concluding game to what had been a riveting series turned into a rout, with Pittsburgh outshooting the Capitals 14-5 in the first period and taking control by scoring twice in the span of eight seconds.
Crosby scored the first of his two goals with 7:24 to play in the opening stanza and Craig Adams followed moments later.
Bill Guerin and Kris Letang scored in the first 2:12 of the second period, both on slap shots, driving rookie Washington goaltender Simeon Varlamov from the game.
Varlamov had been a key factor in bringing Washington back from a 3-1 deficit against the New York Rangers in the opening round, but he gave up four goals on 18 shots in the showdown with the Penguins.
Jose Theodore came on to allow two goals on 12 shots.
Crosby's second goal came on the power play 2:02 into the third period and gave the Penguins a 6-1 lead. Crosby has scored 12 goals in the playoffs and his Washington rival Alex Ovechkin finished with 11.
Ovechkin ended the shutout bid of Marc-Andre Fleury by scoring on a wraparound with 1:51 remaining in the second period. Fleury made 19 saves.
Pittsburgh's opponent in the conference finals will be determined Thursday when Boston hosts Carolina in Game 7 of their series.