The Blues, who won their first two games of the season at home while giving up just two goals, also were victorious in their first road contest to stay unbeaten in the young season.
It is the first time in 20 years St. Louis has won its opening three games.
St. Louis never trailed, getting a first-period goal from Vladimir Tarasenko and a power-play score from David Backes in the second.
Jaroslav Halak, who has been in goal for all of the St. Louis wins, made 26 saves in the victory. He set a franchise record with his 26th career shutout in his previous start last Saturday.
Corey Crawford stopped 31-of-34 shots to take the loss.