Tyler Pitlick and Milan Lucic also scored for the Oilers, who improved to 4-1-0 on the season.
Nail Yakupov replied for the Blues (3-1-1) in his return to Edmonton since he was traded to St. Louis earlier this month.
There was no scoring in the first period, with the Blues getting 10 shots on Oilers goalie Cam Talbot and Edmonton directing eight shots on Jake Allen in the St. Louis net.
The Blues got on the board 3:37 into the second as a scramble allowed Joel Edmundson to feed it in front to Yakupov. It was the second goal of the season for the former Oiler.
