Torey Krug and Justin Faulk scored for the Blues (3-0-0), who are the only undefeated team in the NHL. Binnington got his 11th NHL shutout and first of the season.
"It was a good afternoon in Edmonton," Binnington said. "We have a good team and worked both ways, we did a great job tonight, a full 60 minutes. We were disciplined and it was good to find a way to win in these tight games too."
Jack Campbell made 20 saves, and Connor McDavid had a four-game point streak end for the Oilers (2-3-0).
"It was two good teams in a tight-checking game," Edmonton center Leon Draisaitl said. "They scored two goals and we couldn't get one. They are a good team, that's a playoff team. They have won before, they know how to play a tight-checking game. So did we, I thought, for the most part. But we were a little sloppy in some areas."
Krug gave St. Louis a 1-0 lead on the power play at 5:04 of the first period when he stepped into a pass from Vladimir Tarasenko and one-timed it from the point. St. Louis limited Edmonton to five shots in the period.
"It was a real good effort by everybody on the team," Blues coach Craig Berube said. "I think we limited their rush attack by having a good [third forward] in tight. We checked tonight, that was the difference and our special teams were 100 percent (1-for-1 each on the power play and the penalty kill)."