Brock McGinn's short-handed goal at 12:53 made it 2-0. Carter intercepted a clearing attempt at the blue line and passed to McGinn, whose shot from just inside the right face-off circle trickled through the five-hole.
"We wanted to get puck out of their D-men's hands as quick as we could," McGinn said. "I think 'Carts' made a good [play] reading it up the wall and then getting the puck to me, and I was just fortunate I was able to score there."
Jeff Petry made it 3-0 with a high slap shot from the center point at 15:05.
Johanssen pulled the Capitals within 3-1 at 12:22 of the third period when he scored from the slot off a pass from Sonny Milano behind the net.
Guentzel scored into an empty net at 18:24 for the 4-1 final.
"It was tight both ways. I think any time you play Pittsburgh, it's kind of a game that drags through the mud a little bit," Capitals coach Peter Laviolette said. "There's not a lot of room. It's not pretty. It's not flashy and so we had looks, we had opportunities, finally got one in the third but probably too little, too late."