The Stars (15-14-5) have won five of their last six. Dallas had a four-game win streak snapped with a loss to Toronto on Tuesday.
The Blues (21-11-3) have lost four straight games. They lost in Los Angeles, San Jose and Colorado during a recent three-game road trip.
The Stars scored just 2:08 into the first period after Blues goalie Jake Allen misplayed a puck behind the net and Travis Moen shot it into an open net for his first goal of the season.
The Blues answered 27 seconds later when Alex Pietrangelo’s shot went through Kari Lehtonen’s pads.
The Stars took the lead with 5:14 left in the first period after Ryan Garbutt took advantage of a turnover in the Blues defensive zone and beat Allen with a slapshot to make it 2-1.