Connor Dewar extended the lead to 3-1 at 17:42, redirecting a pass from Lizotte for his first goal this season.
Dewar and Timmins each got their first point since being acquired in a trade from the Toronto Maple Leafs on March 7.
Holloway scored on another St. Louis power play, cutting it to 3-2 at 1:26 of the third period on a one-timer from the right circle.
Rust pushed it to 4-2 at 7:15 when he deflected a Rakell wrist shot from in front.
Toropchenko split the defense for a wrist shot from above the crease after going coast-to-coast, pulling St. Louis to within 4-3 at 8:56.
“We were playing the right way,” Montgomery said. “We had to refuse to be denied. I thought we had that attitude all game long.”
Rakell scored into an empty net at 19:52 for the 5-3 final, reaching 30 goals for the first time since scoring 34 with the Anaheim Ducks in 2017-18.
“It’s a great feeling,” Rakell said. “I love scoring goals. So, obviously, especially with the win tonight, it feels extra good. ... Winning three games for us, it definitely helps us have a good mood around the locker room and on the ice. So, just got to keep it up.”
NOTES: Each of Crosby’s assists came in the third period. It was his 259th multipoint period, passing Gordie Howe (258) for the seventh-most in NHL history, and his 117th multiassist period, ahead of Adam Oates (116) for the seventh-most. ... Blues defenseman Cam Fowler had one shot on goal and one block in 22:19 of ice time. He missed a 2-1 overtime loss at the Los Angeles Kings on Saturday attending to the birth of his second child. ... St. Louis forward Jordan Kyrou had four shots on goal in his 400th NHL game.