Edmonton scored five times on Thursday in a victory against Dallas and the Oilers kept their offense going Friday with two goals that came 23 seconds apart in the opening period.
Jaroslav Halak shut out the Oilers the rest of the way, however, while St. Louis finally got things going.
Jaden Schwartz and Kevin Shattenkirk produced goals for the Blues in the second period to tie it and Sobotka put St. Louis in front 4:28 into the third.
Halak had to make only 15 saves to get the win, the second for St. Louis in three games.
Devan Dubnyk stopped 26 shots for the Oilers, who have lost in each of their last six trips to St. Louis.