Boston defensemen John-Michael Liles and Torey Krug each had two assists, and Tuukka Rask made 25 saves to win for the second time in six games.
The Blues (46-23-9) had a five-game winning streak end. They remained two points behind the Dallas Stars for first place in the Central Division; each team has four games left.
Paul Stastny had a goal and assist for the Blues, and goalie Brian Elliott made 18 saves before being replaced at the start of the third period by Jake Allen, who made four.
"We weren't ready to go," Blues coach Ken Hitchcock said. "We weren't sharp, we weren't ready to go. It was really an extension of the third period of the last game here. We kind of backed off a little bit there and we weren't ready to go tonight. We got going a little bit at periods of time. We had a stretch in the second period where we were good. Obviously a big push in the third period when we scored the third goal, but we weren't sharp, and even saying that, we scored five goals. Some of the goals were really good. They were hard-working goals, but we weren't sharp with the puck and we weren't really sharp in our defending, our communication."