Trent Frederic, a St. Louis native, had two assists, and Linus Ullmark made 35 saves for the Bruins (60-12-5), who have won three straight and 10 of 11, including a 4-3 win against the Pittsburgh Penguins on Saturday.
Boston, which has already won the Presidents' Trophy, has 125 points this season, the most in its history.
"It is something we try not to get caught up in," Marchand said. "But it does speak a lot about the commitment of the team this year, the depth of the group, how great of a job management and the ownership group did putting a really good group together. Teams like this don't come together very often and it is very special to be a part of it."
Jordan Kyrou scored twice, Brayden Schenn had three assists, and Jordan Binnington made 28 saves for the Blues (35-35-7), who were eliminated from Stanley Cup Playoff contention for the first time since 2017-18.
"It's very disappointing," St. Louis coach Craig Berube said. "This organization, and what's expected of everybody, we're not very happy for sure."
Kyrou cut it to 3-1 at 19:51 of the second period, scoring blocker side on a wrist shot from the right face-off circle.
"Late in the second, we're down 3-0," Kyrou said. "We don't have any goals. So, it's a nice boost."
Torey Krug then made it 3-2 at 9:47 of the third period, scoring on the rebound of a shot by Brandon Saad, and Kyrou tied it 3-3 at 19:35 with a shot from the right circle during a 6-on-5.
"Obviously, they had a good start, but we reacted well eventually," said Krug, who played his first nine NHL seasons with Boston. "I thought for the most part we played the right way and guys showed a lot of courage sticking in the fight. We had guys battling through injuries and making big plays at big moments. Unfortunately, we just didn't get the extra point."