Scott Laughton and Ryan Poehling scored, and Carter Hart made 28 saves for the Flyers (24-14-6), who won three road games in the span of four days.
"We just keep on playing," Philadelphia coach John Tortorella said. "Have some good minutes, have some bad minutes, but we just keep on playing.
"Statement games, measure games, I don't believe in that. I just think the team just comes to work, and that's what's good about our group. They come to work each and every day and they attack that day. That's how we've been going about it and that's what we'll continue to do."
Saad and Oskar Sundqvist scored, Brayden Schenn had two assists in his 900th NHL game, and Hofer made 38 saves for the Blues (21-19-2), who went 1-2-1 on a four-game homestand.
"Certainly Joel played well again here today. (He) made some saves, kept it close, gave us a chance to work ourselves into it," St. Louis coach Drew Bannister said. "I think we got what we deserved. For 40 minutes we didn't have enough effort in our game in hard areas. We continue to mismanage the puck that is making it difficult on our team. We have to defend, which makes it easy for them. More offensive zone time, more shots at the net.
"First two goals, we turn the puck over in the offensive zone, it goes down and it's in the back of our net. Those plays can't happen. We've got to make better decisions there."