Pyorala's goal in the fourth round was the difference as the Flyers won their fourth consecutive game. Philadelphia's Claude Giroux and St. Louis' Brad Boyes each scored in the first round.
Scott Hartnell scored in regulation for Philadelphia, which moved to 83-39-17 overall against the Blues, including 47-12-10 at home.
The struggling Blues, who entered with the NHL's fourth-worst record, have dropped four straight.
Hartnell gave the Flyers the lead with 7:45 remaining in the second period. Streaking down the left side, he deflected Giroux's cross-ice pass past Chris Mason.
Hartnell's momentum carried him into the net, and officials reviewed the goal to determine whether he kicked the puck as he slid.
St. Louis (5-7-2) tied it in the third when T.J. Oshie corralled Roman Polak's blue-line shot and flipped it past Emery at 5:43.
The Flyers (9-4-1) almost grabbed the lead again midway through the third. Mason stopped Hartnell's rebound attempt but his glove appeared to be behind the line in TV replays. The play wasn't reviewed.
Hartnell also nearly won the game in overtime with some nice stick work, but Mason made a sprawling save.
In his first career game against St. Louis, Ray Emery stopped 30 shots. Mason, who shut out the Flyers in their only meeting last season, had 35 saves.
NOTES: Philadelphia's Chris Pronger, who spent 1996-2004 with the Blues, had an assist. He now has a point in nine of his 12 games, and 14 points overall - three goals and 11 assists.