Jason Akeson also scored for the Flyers, who failed to advance to the postseason for just the ninth time in franchise history.
Kyle Turris scored for the Senators and Craig Anderson stopped 23 shots.
The loss leaves the Senators sitting eighth in the Eastern Conference. They can finish seventh if they pick up a point against the Boston Bruins in the season finale Sunday.
The Flyers took a 2-1 lead midway through the third when Voracek beat Anderson with a wrist shot to quiet the 20,232 on hand.
The Senators continued to struggle on the power play, going scoreless on five opportunities.
Ottawa tied the game early in the second as Turris was able to find just enough room short side to beat Mason. The goal came as a result of some good work down low by Chris Phillips and Colin Greening.
Phillips picked up his 200th NHL career assist on Turris' goal.
The Senators were the better team in the first, outshooting the Flyers 14-5 and dominating play, but some sloppy play by the Senators in their own end led to Akeson scoring his first NHL goal in his first game in his home city.
Anderson made an initial save on Claude Giroux, but he and defenseman Erik Karlsson were both unable to clear the rebound, leaving the puck waiting for Akeson.