CHICAGO -- Jason Bacashihua will have to wait for his first NHL shutout.
Kyle Calder scored with 4:32 left for the Blackhawks, who lost their fifth consecutive game and seventh in their last eight.
"I'm still looking for it," Bacashihua said. "You get under five minutes there, but I'm sure it will come. We've just got to bear down in the last 10 minutes and make sure we make the right plays. But we we're able to hold them off and get another win."
Brewer and Drake scored late in the first period to stake Bacashihua to 2-0 lead.
Bacashihua had to make only a handful of tough saves against the struggling Blackhawks, who have scored only 10 goals during the five-game losing streak.
Calder finally broke through when he was left alone in front of the Blues' net. After taking a pass from Tyler Arnason, Calder spun and slid in a low shot.
"He made a couple of key saves tonight," Blues coach Mike Kitchen said. "He had a very strong game. He was very efficient in his net. He had a lot of good, short, direct moves and was able to make the second saves."
Bacashihua also benefited from having a lead.
"The way we started the game was the most important factor for us tonight," Kitchen said. "It's one of the areas we've struggled in all season. We showed them from the drop of the puck we wanted to win the game."
Bacashihua made his sixth consecutive start and seventh appearance in a row for the Blues after being recalled from Peoria of the AHL on Dec. 12. He made his NHL debut Dec. 16 against the Blackhawks, replacing Curtis Sanford early in the second period after Sanford was injured.
"It's exciting," Bacashihua said. "A lot of kids dream of being a No. 1 and right now I'm that guy. I just can't let it go to my head. I've just to keep playing well and playing hard."
Nikolai Khabibulin started in goal for the Blackhawks, but left after two periods because of pulled groin. Chicago coach Trent Yawney said he didn't know how long Khabibulin will be out.
Khabibulin allowed two goals on 22 shots through two periods. Craig Anderson played the third period, stopping all 10 shots he faced.
"There are a few aspects of the game where we've really got to grow up and it showed tonight, like the sticking penalties," Blackhawks captain Adrian Aucoin said. "We have to understand we're not going to win unless we all play together, unless we all take shorter shifts, unless we put the puck on the net and unless we play as a five-man unit."
Brewer converted a rebound of Scott Young's shot from the slot with 2:16 left in the first period to open the scoring.
Moments earlier, Khabibulin had stopped Brewer on a breakaway, set up when Brewer took a long lead pass directly after leaving the penalty box.
Following the breakaway attempt, Brewer fed a loose puck from behind the net to Doug Weight, who passed to Young. Khabibulin blocked Young's shot, but Brewer was still lingering at the edge of the crease and slipped the puck between Khabibulin's pads.
Drake's power-play goal with 43 seconds left in the period gave St. Louis a 2-0 lead. Drake closed in from the right circle, took a feed from Petr Cajanek and beat Khabibulin high on the stick side.
Bacashihua stopped a close-in chance by Jaroslav Spacek during a Chicago power-play early in the third. A few seconds later, Anton Babchuck's stick broke on a close-in attempt.
The rookie goalie made a diving glove save on Tyler Arnason's rebound attempt during a Chicago power-play midway through the third.
St. Louis defenseman Bryce Salvador sat out because of the flu. Blues forward Simon Gamache and defenseman Kevin Dallman were healthy scratches ... Chicago forward Pavel Vorobiev was a healthy scratch. Blackhawks defenseman Jassen Cullimore missed his ninth game with a groin pull. He is expected to return in the next few days.