Boucher stopped 28 shots for his 13th NHL shutout and first victory with the Blackhawks, a 1-0 win over the Columbus Blue Jackets on Sunday night.
"It's a huge sense of relief, but it wasn't getting to my head," said Boucher, 1-7-1 this season. "You know you can win. It's just a matter of getting that first one."
Defenseman Lasse Kukkonen scored in the second period to help the Blackhawks win their second in a row following an 0-7-1 slide.
"We definitely didn't give up a lot," Chicago coach Trent Yawney said. "Even with the penalties, we kept them (Columbus) to the outside. And when we needed Bouche, Bouche was there for us. It was nice to see him get the win. He deserves it."
Chicago also gained a point in a shootout loss in New Jersey on Thursday night and is 2-0-1 in its last three.
"A 1-0 game's not what the league wants, but it was a good win for us and a good weekend," Boucher said. "We got five out of six points and we're going in the right direction here."
Columbus' Fredrik Norrena made 18 saves. The Blue Jackets have lost two in row and are 1-3-0 in their last four.
"These are two teams plugging for points and they are battling and playing pretty tight, defensive games," Columbus coach Gerard Gallant said. "Just going by our video guy, the chances were like 11-5, so it was a low-scoring, boring type of game. I thought we had the better team tonight for sure, but we got the short end of the stick."
Thanks to three power-play chances, Columbus dominated territorially in the scoreless first and outshot Chicago 10-4.
The Blackhawks took the game's first five penalties and were forced to kill two brief 5-on-3 disadvantages early in the second.
"We're playing well in all three zones and showing a lot more desperation," Boucher said. "We're blocking a lot more shots and the PK is unbelievable."
Kukkonen scored the only goal at 7:04 of the second.
He fired a shot through a screen from between the circles after taking a centering pass from Bryan Smolinski. Chicago's Martin Lapointe jumped straight into the air to allow Kukonnen's low drive to reach the net and slip between Norrena's pads.
"It was a great pass from Smoke," Kukkonen said. "Marty just got out of the way and the goalie didn't see anything."
Chicago forward Rene Bourque left the game late in the second period after being cut in the neck by the Columbus right wing Nikolai Zherdev's skate blade during a pileup in the Blackhawks' crease. According to team officials, Bourque was in stable condition when he was taken to The University of Chicago Hospital.
"We know he's stable. He's OK and it's not life-threatening," Yawney said.
- Top Blackhawks goalie Nikolai Khabibulin, sidelined since Oct. 21 by a broken finger, could return Thursday at Phoenix as Chicago begins a five-game western road trip.
- Chicago F Martin Halvat, out since Oct. 20 with a sprained ankle, has resumed light skating but may not return until December.
- Blackhawks LW Tony Salmelainen missed his fifth game because if a separated shoulder.