Marc-Andre Fleury made 32 saves for his fifth shutout of the season and 28th of his career.
The Penguins swept the home-and-home series, winning the opener 3-2 on Monday in Washington. They have outscored the Capitals 30-14 in the eight games since Washington's last win in the series (1-0) on Jan. 11, 2012.
Crosby extended his NHL lead with his 88th point. He scored his 31st goal of the season on a wrist shot from the right circle that beat Jaroslav Halak on the far side with 5:48 remaining to give the Penguins a little insurance.
Halak allowed two goals on 34 shots and the Capitals lost for the fifth time in their last six games.
The Eastern Conference-leading Penguins swept the season series 4-0.
Fleury had six saves in the first and second periods, then made 20 in the third to keep the Capitals off the board.
One of Fleury's saves came on his stomach as he threw his right skate out to block a shot from Capitals newcomer Evgeny Kuznetsov that ricocheted off the post.
Kuznetsov played his first two NHL games in the home-and-home after the Caps signed the Russian forward to an entry-level contract on Saturday, plucking the 2010 first-round draft pick from the Kontinental Hockey League.
"The second half of the game they really came at us," said Crosby. "To keep them off the board was important ... especially when they're hanging around when it's 1-0. A lot can happen."
The first period was played at a brisk pace and the first whistle didn't come until there was 5:36 left when Halak covered the puck in the crease.
"We were on our heels the hole first period, no question," said Capitals coach Adam Oates. "We turned it over too many times -- probably a little hangover from (Monday) night."
Jokinen scored soon after that, with 3:19 remaining, when he deflected Matt Niskanen's point shot through Halak to give the Penguins a 1-0 lead.