Marc-Andre Fleury made 36 saves for the Blackhawks.
"All I want is a win," Fleury said. "It doesn't matter how we get it. It was nice not to give up four or five or six goals. The guys helped me out tonight. As a team, we defended better. It showed on the scoreboard."
Krug scored a power-play goal at 7:25 of the third, a shot from the right circle that caromed off Blackhawks defenseman Seth Jones and changed direction past Fleury for a 1-0 lead.
The Blues went on the power play when DeBrincat tripped center Brayden Schenn from behind, sending Schenn crashing into the boards in the St. Louis zone.
"My stick got stuck in a skate and they get a power play," DeBrincat said. "It can go the other way too. Unfortunately, it happened to us."
The Blues worked the puck over to Krug in the right circle. Krug was actually trying to pass to forward Robert Thomas at the back post before the puck changed direction.
"Yeah, that's exactly what was going on," Krug said. "I didn't like the way the power play ... we were just kind of passing the puck around and not getting anything at the net. ... I had to throw it there at the net and make a play."
Binnington's toughest save came off a Dominik Kubalik breakaway 1:28 into the second when he kicked out the right pad.
"At that point in the game, Fleury was making some big saves," Binnington said. "We were kind of putting the pressure on them. He's a goal scorer, coming down. Good shooter. Kind of just came out and challenged and played it and stopped it. So it was good.
"It was kind of back and forth. Not many whistles, it felt like. It was intense. It was exciting. It was Saturday. It's nice when you win."
NOTES: Schenn left the game after he was tripped, came back for a short shift, only to be sent back by concussion spotters, according to coach Craig Berube, before returning to the game. … The Blues have shut out the Blackhawks the past two games and have a 131:44 shutout streak against Chicago. ... St. Louis forward Vladimir Tarasenko had an assist to extend his point streak to six games (four goals, five assists). ... Binnington's last shutout was Feb. 20, 2020, against the Arizona Coyotes, also a 1-0 win. ... The Blues have won five straight against the Blackhawks, outscoring them 17-8.