The Blackhawks limited the Stars to five shots on goal in the third period after allowing 22 through the second.
"We blocked a lot of shots, a couple late where they had good position in the slot," Crawford said. "Just seemed like our overall game was great tonight."
Klingberg said, "They did a pretty good job taking the puck out of our hands today. I feel like we rimmed or dumped a lot of pucks, and then we were chasing it and we didn't get a lot of possession time."
The Stars did not have a power play for the first time this season.
"Especially with the way the kill's been going, that's huge for us," Kunitz said. "That means guys were working. We're skating. We're keeping our sticks down."
Chicago allowed seven power-play goals in 23 times shorthanded in its previous 10 games.
After Khudobin was pulled for the extra attacker with 1:15 remaining, Stars captain Jamie Benn was called for interference with 16.6 seconds remaining, forcing Khudobin back into the net.
Crawford is 3-1-0 with a 3.44 goals-against average and .886 save percentage in three games since returning after missing 28 games with a concussion.
"It's a process. It's a challenge," Crawford said. "It's not easy. This league is fast. You've just got to work hard and keeping going to try and get the timing. I feel like it gets even harder after that."