Blues coach Ken Hitchcock yanked goalie Brian Elliott in favor of Jake Allen after the Stars took a 3-0 lead before the midway mark of the first period, the last two goals coming in a 20-second span.
Jason Spezza had three assists for the Stars, who have won four of five and triumphed on coach Lindy Ruff's 55th birthday. Dallas entered 11th in the Western Conference with 60 points, 18 behind St. Louis.
Patrik Berglund spoiled Lehtonen's bid for a second straight shutout with 7:30 remaining. Lehtonen's scoreless streak was 1:45:48.