Monahan scored on the power play 3:24 into the second period to make it 4-1 when he shot by Binnington's blocker, and Blake Coleman pushed the lead to 5-1 at 14:11.
Adam Ruzicka extended it to 6-1 at 16:09 when he finished a three-way passing play with Tkachuk and Gaudreau, and Gaudreau made it 7-1 at 19:36 with a shot glove side on Binnington off a partial breakaway set up by Tkachuk.
"He's making plays out there," Gaudreau said. "Obviously smart player. He can see the ice really well, uses his teammates, and he made some big plays tonight."
The two teams play again in St. Louis on Thursday, on the second night of a back to back for the Flames.
"We have to play them again here right away," St. Louis coach Craig Berube said. "We're going to take some stuff out of [the game], learn from it, and move on and play a better game the next time we play them."
NOTES: Gaudreau, who has at least 30 assists in eight straight seasons, is seventh in the NHL in assists since the start of the 2014-15 season (356). ... Tkachuk, who is from St. Louis, has scored 17 points (four goals, 13 assists) in 12 games against the Blues. The Flames forward was one assist shy of tying Guy Chouinard and Gary Suter's franchise record for the most in a game. ... Flames defenseman Erik Gudbranson, who assisted on Zadorov's goal, played in his 600th NHL game. … Tanev's goal, his second of the season, ended a 31-game drought. His first goal was Oct. 25 in a 5-1 win against the New York Rangers.