Marc-Edouard Vlasic and Devin Setoguchi also scored for the Sharks, who finished their three-game road trip 2-1 after back-to-back wins.
David Backes scored the only St. Louis goal on a penalty shot in the second period, and the Blues lost for the third time in four games.
The Sharks took a 2-0 lead in the first period against a good home team in St. Louis.
Couture deflected a Dan Boyle slap shot on a power play for the first goal at 9:30, and Vlasic beat Jaroslav Halak with a fluttering shot from the left side at 18:15.
Halak allowed the two first period goals on just seven shots and was beaten by another Couture deflection at 8:21 of the second period.
St. Louis got its only goal when Backes' soft wrister got through Niittymaki midway through the period, pulling the Blues within 3-1.
San Jose ended the scoring when Halak gave up a rebound in the crease and Setoguchi was there to stuff it home.
The Blues fell to 10-3-2 this season at Scottrade Center...San Jose was 1- for-4 on the power play, while St. Louis was scoreless on its only opportunity.