Robert Thomas scored to extend his point streak to 14 games, Pavel Buchnevich had a goal and an assist to extend his point streak to 11 games, and Vladimir Tarasenko had two assists for the Blues (46-20-11), who extended their point streak to 13 games (11-0-2). Ville Husso made 32 saves.
"We got a big point there, which is good and in our in our fight for home ice, but you know, definitely wasn't our best effort tonight," St. Louis captain Ryan O'Reilly said. "... It just wasn't our best game, that's for sure."
St. Louis is tied for second in the Central Division with the Minnesota Wild, who defeated the Montreal Canadiens 2-0 on Tuesday. Minnesota has one game in hand.
"We've got to stay consistent," Blues coach Craig Berube said. "There's home ice on the line, there's a lot to play for."
Buchnevich gave St. Louis a 1-0 lead at 11:49 of the first period, redirecting a centering pass from Tarasenko in the slot on the power play.
DeBrusk tied it 1-1 at 1:33 of the second period. After Matt Grzelcyk intercepted a clearing pass from Colton Parayko, DeBrusk skated out from behind the net and roofed his own rebound off a wraparound attempt.
Hall put the Bruins in front 2-1 at 9:44 when he redirected Derek Forbort's shot from the left point.
Boston held a 17-9 advantage in shots in the second and carried a lot of the play in St. Louis' zone.
"Sometimes you get a team when they're on a winning streak, they're winning games at the end of it because they're making plays," Cassidy said. "I thought if we put a lot of pressure on them and didn't give them a lot of time and space, we play to our strength because they've been scoring a lot of goals and maybe frustrate them. I saw a little of that in the second period. We were able to get on top of them, and that can maybe put a team on its heels."