The Blackhawks remained six points behind the Vancouver Canucks, Nashville Predators and Winnipeg Jets for the first wild card into the Stanley Cup Playoffs from the Western Conference.
"Tough," Blackhawks coach Jeremy Colliton said. "We need those two [points], obviously. But I got no complaints for the work ethic of the team. I thought they competed really hard."
Robert Bortuzzo collected a loose puck at the side of the net and scored to give the Blues a 1-0 lead at 6:41 of the second period.
"That's like 13-, 14-year-old outdoor rink stuff," Bortuzzo said after ending a 13-game goal drought. "I've worked that out of my game actually, but sometimes they pop up once in a while. Fortunately, [I] got to bury one."
Schwartz sent a cross-ice pass to Alex Pietrangelo inside the left face-off circle, where he scored at 5:37 of the third for the 2-0 final.
Chicago had one shot on goal in four power-play opportunities.
"Pucks maybe weren't bouncing our way, maybe we weren't working hard enough to put it in the net," Blackhawks forward Alex DeBrincat said. "You're obviously a man up and you need to convert on those chances."
It was Allen's second shutout of the season; each has come against the Blackhawks. He made 38 saves in a 4-0 win at United Center on Dec. 2.
St. Louis won all four games against Chicago this season.
"It's pretty cool," Allen said. "Obviously they're our biggest rival to date; we play them a lot. They got the best of us there for a while. It's good to get some wins under our belt. The rivalry's still going to go on for a long time. It's going to be fun moving forward."
