Guttman then scored on a wrist shot from the inside of the right circle, tying it 2-2 at 10:05 of the third.
Dickinson dove at a pass from Perry for a shot that put Chicago ahead 3-2 before Foligno scored an empty-net goal for the 4-2 final at 18:33.
"We worked the whole game,” Blackhawks coach Luke Richardson said. “I thought we had great scoring chances in all three periods. ... We got some key execution in the third period, especially. I thought we played excellent after that. We played simple, fast."
Rust put Pittsburgh ahead 1-0 at 7:04 of the first period, deflecting a shot from Kris Letang at the right of the net. The goal was initially waved off before a review determined the puck ricocheted out after hitting inside the top of the net.
Crosby made it 2-0 at 11:56 of the second period. Jake Guentzel sent a pass through the slot to the bottom of the left face-off circle, setting up Crosby for a wrist shot. The goal was confirmed by video review after Chicago challenged for offside.
“It’s Game 1, so you have to learn,” Crosby said. “It’s better when you can learn when you’ve won. … It’s just who can get to their game a little bit better. Obviously, they were able to get a couple there in the third.”