Alexander Steen brought the Blues within 4-3 at 11:30, but Anderson scored 38 seconds into the third to make it 5-3, and Duclair on the power play at 2:35 made it 6-3. Jones, who missed the first seven games with a Grade 2 MCL sprain of his right knee before making his debut Tuesday, scored at 6:03 to make it 7-3.
Zach Sanford scored at 12:36 to pull the Blues within 7-4.
Tarasenko's first goal in seven games, on the power play, gave St. Louis a 1-0 lead at 4:26 of the first. Jaden Schwartz's first goal of the season at 12:40 made it 2-0.
"It's frustrating, for sure," Steen said. "I don't know what to say. It's not good enough, obviously. We're going to get back to work tomorrow. We can't feel sorry for ourselves."