Jimmy Snuggerud and Jake Neighbours also scored for the Blues (6-6-1), who lost 4-0 to the Carolina Hurricanes 4-0 on Saturday and 2-0 to the Montreal Canadiens on Tuesday. Joel Hofer made 31 saves to help St. Louis end a five-game homestand at 3-2-0.
James Hagens scored for the Bruins (9-4-1), who have lost two straight after an eight-game point streak (7-0-1). Jeremy Swayman made 14 saves.
St. Louis scored four straight goals after falling behind early in the first period.
Snuggerud tied it 1-1 on the power play at 15:43 with the Blues’ first goal in a span of 139:38. Thomas won a face-off in the right circle to Broberg, who moved the puck to the middle of the ice and passed to Snuggerud for a one-timer from the left circle.
Broberg made it a 2-1 lead at 5:17 of the second period. Connor McMichael brought the puck out from behind the net on the right side and fed Broberg for a wide-open wrist shot from the high slot that beat Swayman bar down in the top right corner.
Thomas extended it to 3-1 at 12:08. He spun at the offensive blue line, moved into the high slot and beat Swayman with a wrist shot into the top left corner.
Neighbours pushed the margin to 4-1 with a power-play goal at 12:42 of the third period. After another Thomas face-off win, Broberg’s shot from the top of the slot was blocked, but Neighbours slipped the loose puck through Swayman’s five-hole.
Hagens gave the Bruins a 1-0 lead at 5:28 of the first. Casey Mittelstadt picked off Hofer’s pass up the boards and sent the puck in from the left side before Hagens redirected it past the glove.