Jordan Eberle and Nail Yakupov both netted twice, with Taylor Hall, Ryan Whitney, Sam Gagner and Ryan Nugent-Hopkins also on target and Matt Stajan responding with two goals for Calgary.
Edmonton have won five straight games and lead ninth-placed St Louis by one point but have played two more games.
The only team on a longer winning run in the NHL are the San Jose Sharks, who clinched a sixth successive victory as they saw off the Minnesota Wild 4-2.
New recruit Ryane Clowe scored twice in the New York Rangers' 6-1 win over the Pittsburgh Penguins, who have lost two games back-to-back after their 15-game winning streak.
The Anaheim Ducks downed the Dallas Stars 5-2, while the Philadelphia Flyers posted a 5-3 win against the Montreal Canadiens.