Darryl Sittler, Glen Cochrane and Brian Propp each scored once to enable the Flyers to win in Philadelphia.
The Blues haven't won in the Spectrum in 26 tries since Jan. 6, 1972.
Cochrane was an unlikely contributor to the scoring. It was his first goal of the season.
"Any time Glen scores, it's an accomplishment for all of us," Flyers Coach Bob McCammon said.
"I thought we were a little too cautious when we got the lead, but I believe that's because we got blitzed at the end in Montreal," McCammon added, referring to Saturday night's 6-4 loss to the Canadiens.
Sittler put the Flyers ahead, 1-0, at 3:08 of the second period, beating Glen Hanlon from the center of the left faceoff circle for his 11th goal.
Brian Sutter tied it at 17:20 with his 14th goal. He followed up Bernie Federko's 55-foot slap shot and put the rebound past goalie Pelle Lindbergh. The tie lasted only 1:19. Cochrane scored on a 58-footer, deflecting it in off a St. Louis player at 18:39.
The Flyers, who outshot the Blues, 45-23, got an insurance goal at 10:47 of the third period when Propp put the puck behind Hanlon, who had fallen, for his 10th goal.
Emile Francis, the St. Louis coach and general manager, said the Flyers' mastery over his team was not a mental factor.
"Most of these players have not been around long enough to think about that," he said. "Our goaltender was outstanding, and so was our defense, but we just didn't get enough opportunities to score.''