Defenseman Alex Pietrangelo, the No. 4 pick in this year's NHL draft, had two assists for the Blues. Pietrangelo is one of several players auditioning to take former top overall pick Erik Johnson's spot in the lineup.
The Blues announced before the game that Johnson tore two ligaments in his right knee while driving a golf cart during a team outing and would likely miss the entire season.
Loui Eriksson and Sean Avery scored for Dallas, which played its preseason opener.
Blues starting goalie Manny Legace played the first 30 minutes, 25 seconds and made six saves on seven shots. St. Louis improved its preseason record to 1-1.
Stempniak gave the Blues a 2-1 lead, scoring during a power play with 2:23 left in the first period. Boyes, who led St. Louis with 43 goals last season, made it 3-1 at 2:17 of the second with another man-advantage goal.
Avery scored off a scrum in front with 3:59 left to cut it to 3-2.