The goal came on the Blues' 20th shot of the period after coach Craig Berube switched up the lines.
"It was better," Berube said. "I thought there was some good stuff around the net, rebound action. Their goalie played well, so did ours.
"[Skinner] made a couple saves and we missed the net a couple times on that. It's close, even with the goalie out, we had a couple good looks. You've just got to stick with it. Goal scoring's funny sometimes. You dry up sometimes. I know it doesn't happen to us a lot sometimes, but right now, it's at that point. We've got to simplify it and we've got to get some dirty goals. That's the bottom line."
Hyman scored into an empty net with 27 seconds remaining for the 3-1 final.
"I think we should be happy," Nugent-Hopkins said. "We had a few little breakdowns. We had 'Stu' when we needed him and the D-men made some big plays. We found a way to break them down. The first [road game] was a good one. We just have to keep on doing it."
NOTES: Oilers forward Leon Draisaitl had an assist to give him 19 points (six goals, 13 assists) in 19 games against the Blues. ... St. Louis is the only NHL team McDavid isn't averaging a point per game against; he has 17 points (six goals, 11 assists) in 20 games for an average of 0.85 points per game. ... The Blues penalty kill was 2-for-2 and is 11-for-11 this season. They are one of two teams (New York Islanders) to not have allowed a power-play goal. St. Louis also matched its record for consecutive kills to begin a season, also done Oct. 3-5, 2013 and Oct. 1-3, 1997. ... Schenn has 22 points (eight goals, 14 assists) in 21 games against Edmonton.