Bishop started for the first time in two years last Monday against Chicago and gave up four goals on eight shots before being removed from the game.
He turned that around in a hurry Friday, keeping the Oilers off the board while the Blues were halting a three-game losing streak. Bishop had picked up a win in relief against Anaheim last week.
Chris Stewart scored his 17th and 18th goals of the season to highlight the St. Louis offense.
Stewart opened the scoring 2:07 into the contest and his power-play goal 4:19 into the second gave St. Louis a 3-0 lead.
Patrik Berglund, Roman Polak and Matt D'Agostini also scored for the Blues.
Devan Dubnyk allowed the five goals on 22 shots. Edmonton had won four of its previous five games.