Alexander Romanov scored at 1:57 of the third period to make it 3-1 off a giveaway by the Blues behind their net.
It was Montreal's first goal since Jonathan Drouin scored at 7:08 of the second period in a 3-2 loss against the Tampa Bay Lightning last Tuesday, a stretch of 134:49.
"We came out pretty good in the third, had chances to get back in the game after we score the first one," Canadiens forward Joel Armia said. "We had chances after that too to score a goal, but it just didn't go in."
Torey Krug scored a power-play goal on a slap shot from the top of the left circle at 10:16 of the third for the 4-1 final.
NOTES:Allen was 148-94-26 with a 2.50 goals-against average, a .913 save percentage, and 21 shutouts with the Blues; he is second in Blues history in wins (Mike Liut, 151) and shutouts (Brian Elliott, 25). ... Armia played 16:37, had four hits and was a minus-1 in his return after missing two games with an undisclosed injury. ... The home winning streak for the Blues is their longest since winning nine straight from Dec. 12, 2019-Jan. 13, 2020. ... Blues forward Jordan Kyrou left the game late in the second period with an undisclosed injury and Berube said he will know more Sunday if Kyrou would be available to play against the Anaheim Ducks. ... The Blues were 2-for-3 on the power-play and are third in the NHL at 29.9 percent.