Cody Eakin had a goal and assist and Kari Lehtonen was strong in net for the Stars, who have won four of five in pursuit of a Western Conference playoff spot.
Dallas entered the day three points out of a playoff spot before winning for the second straight night and saddling the Blues with just their sixth regulation home loss.
Alex Steen had a pair of power-play goals for the Blues, who had been 8-0-2 in their previous 10 at home including an overtime loss to Dallas earlier this month. St. Louis fell one point behind Boston for first place overall in the NHL.
[He's] real confident with the puck now, getting it off his stick quick and no second-guessing. We need that. He's such a good guy in the room. He works so hard. That's the big thing. For not a big man, he just fights for every puck and when he scores, the guys appreciate that even more.
— Winnipeg Jets coach Paul Maurice on Mathieu Perreault, who scored two goals in win against Chicago Blackhawks on Tuesday