Andy McDonald scored a pair of goals and the 1, to take over sole possession of first place in the Central Division.
The Blues entered Tuesday's action tied with Detroit for the top spot in the division. With the Red Wings falling to the Flyers on Tuesday, St. Louis stands alone in first with 91 points.
"It's exciting but we realize there is a lot of hard work left," McDonald said. "Most importantly we have to make sure we are getting our game to a spot where we are ready for the playoffs and we're improving and we're not kind of coasting into the playoffs."
Vladimir Sobotka, T.J. Oshie and Jason Arnott also lit the lamp for the Blues, who have won two in a row and six of seven. Jaroslav Halak made 19 saves.
Andrew Brunette scored the lone goal for the Blackhawks, who had a three-game winning streak snapped.
Ray Emery stopped 26-of-31 shots for Chicago, which sits sixth in the Western Conference with 79 points.
The Blues got on the board at the 5:13 mark of the first period. Carlo Colaiacovo's blast from the left point was deflected in by Oshie.
McDonald's power-play goal with 37.6 seconds left made it a 2-0 contest. McDonald carried the puck down the right wing and threw a backhander on net that hit off a Chicago player and went into the net.
St. Louis scored a short-handed goal at the 1:46 mark of the middle stanza. Scott Nichol controlled the puck at the left point and slid a nice pass to Sobotka, who got behind the defense. Sobotka's backhander beat Emery to make it 3-0.
Halak made 11 saves in the second frame to preserve the three-goal cushion.
"They are a tough team to get down to," Chicago forward Viktor Stalberg said. "When they score first they're pretty good. They don't give up too much and they're pretty good at playing a structured hockey game. We certainly wanted a better start tonight."
Chicago finally got on the board at the 1:58 mark of the third. Brent Seabrook's shot from the right point was deflected in by Brunette.
McDonald and Arnott scored in the final five minutes to turn the game into a rout.
Chicago and St. Louis have split four meetings this season...The Blues improved to 27-4-4 at home this season...The Blackhawks went 0-for-5 on the power play...St. Louis defenseman Kent Huskins (hand) missed the game...The Blackhawks went 2-1-0 on a three-game road trip...Chicago captain Jonathan Toews (upper body) missed his eighth straight game and defenseman Niklas Hjalmarsson (concussion-like symptoms) sat out his fifth straight contest.