Robert Thomas, Jay Bouwmeester and Sammy Blais also scored for St. Louis, which won for the second time in its last six home games.
Binnington improved to 2-0 after becoming the 35th goaltender in NHL history to record a shutout in his first career start on Monday at Philadelphia.
Veteran Carey Price, meanwhile, allowed four goals on 30 shots to lose his third consecutive start.
Thomas scored his fifth of the season on the power play 1:56 into the game when he pushed Ryan O’Reilly’s rebound past Price. The Blues had scored on just one of their previous 20 power plays.
Sundqvist buried a feed from O’Reilly for his eighth goal of the season to extend the St. Louis lead.
Bouwmeester put the Blues ahead 3-0 when he skated in front of the defence and converted a feed from Robby Fabbri 6:04 into the second period.
Three minutes later, Brendan Gallagher spoiled Binnington’s shutout bid when he scored his 17th goal of the season on a power play.
Blais scored his first goal of the season 9:19 into the third period.
NOTES: Blues D Carl Gunnarsson recorded his 100th career assist on Sundqvist’s goal. … RW David Perron has registered at least one point in his last nine games. … Canadiens D Karl Alzner skated in his first NHL game since Nov. 24. He had been a healthy scratch for seven games since being recalled from the Laval Rocket of the AHL.
Canadiens: Host Colorado on Saturday.
Blues: At Dallas Saturday to open a four-game trip.