Jeff Carter added his 25th goal for the Flyers, who increased their Atlantic Division lead over Pittsburgh to three points.
Brenden Morrow scored for the Pacific Division-leading Stars in the second period, his fifth goal in six games.
In a matchup of division-leading teams, Meszaros scored with 1:20 left in the first period. He took a feed from Ville Leino and flipped a wrist shot over Kari Lehtonen's glove.
Powe added to the lead 1:19 into the second with a short-handed wrister from the center of the circle. It was his first goal since Nov. 15, a span of 35 games. Like Meszaros' goal, Lehtonen anticipated low, but was beaten with a high shot.
The short-handed goal was the eighth for the Flyers, tying them for second in the NHL behind the New York Rangers. It was the ninth given up by the Stars, tying them for second-worst.
Blair Betts recorded his seventh assist on Powe's goal, his first point since Nov. 26.
Morrow scored for Dallas at 12:07 of the second, deflecting Mike Ribeiro's shot past Boucher's glove side.
Carter scored the final goal for Philadelphia when he slapped a bouncing puck into the left corner of the net for his fifth goal in five games.
Lehtonen stopped 29 shots and fell to 0-10-1 in 11 games against Philadelphia.
The Flyers, who lead the league with 35 wins, are 12-3 in 2011. They are 28-1-2 when leading after two periods.
The Stars, who have lost three straight, limped into Philadelphia following a 6-3 defeat at Boston on Thursday in a game in which they had three fights in the first 80 seconds.
Notes: The Stars haven't won in Philadelphia since Dec. 1, 2007, and are 39-67-32 against the Flyers. Philadelphia has won the past four meetings. ... Flyers D Braydon Coburn played in his 350th NHL game. ... Stars forwards Toby Peterson (lower body), Tom Wandell (shoulder) and Adam Burish (face) all sat out. ... The Flyers are one of four teams with a goal differential of at least plus-40.