Kyrou put St. Louis ahead 1-0 at 2:04 on a breakaway after taking a stretch pass from Nick Leddy. Hofer had the secondary assist.
"It just all happened so fast," Kyrou said. "Just kind of just instinct."
Kyrou scored again 42 seconds later to make it 2-0, converting on a 2-on-1 with Brandon Saad. Kyrou kept the puck and beat Mrazek short side with a wrist shot from the left face-off circle.
"I was trying to pass (to Saad) the whole time and then last second, I decided to shoot," Kyrou said.
Torey Krug extended it to 3-0 at 4:37 on a shot from the point that got through traffic, chasing Mrazek. It was Krug’s first goal since March 2 (17 games).
"We definitely weren't ready to compete and they showed their desperation on where they are in the standings," Blackhawks coach Luke Richardson said of the Blues. "And unfortunately, we didn't give Petr much help, giving him a breakaway and a 2-on-1 to start the game."
Bolduc pushed it to 4-0 at 6:59 on a one-timer from the right of the goal line off a cross-crease pass from Thomas. It was the first shot against Soderblom.
"Obviously, we had a real good start to that game and got rewarded, broke the game open pretty quickly," St. Louis interim coach Drew Bannister said. "Good to see our guys come out with that kind of urgency to start the game."
Philipp Kurashev cut it to 4-1 at 8:40 of the second period when he got to a rebound at the right side of the net after Kevin Korchinski's shot caromed off the end boards.
Thomas made it 5-1 at 10:01 of the third period, putting in the rebound of Schenn's one-timer from the right circle.