The Blues answered with three goals in the second period to take the lead.
Broberg cut it to 2-1 at 1:40 with a wrist shot from the left point that went in off Soderblom’s glove, and Nathan Walker tied it 2-2 just 10 seconds later when he intercepted an Ethan Del Mastro pass and scored from the high slot.
Joseph gave the Blues their first lead when he finished at the top of the crease off Brayden Schenn's pass from behind the net to make it 3-2 at 17:09.
“I just felt like we gave too many odd-man rushes, especially with a team on back-to-back,” Schenn said. “You’ve got to play to the goal line, and we got to that in the second period.”
Martinez tied it 3-3 at 3:50 of the third period on a one-timer from the right circle off a pass from Teravainen.
Cam Fowler responded to put the Blues back in front when his shot from the left point deflected in off Blackhawks defenseman Seth Jones to make it 4-3 at 4:32.
Teravainen's one-timer from the right circle deflected in off Blues defenseman Ryan Suter to tie it 4-4 at 6:08.
Mikheyev raced into the offensive zone around Blues defenseman Justin Faulk before tucking a backhand through Binnington’s pads to give Chicago a 5-4 lead at 11:08.