Claude Giroux had a goal in the second round for the Flyers, but Mike Ribeiro tied it for Dallas in the third round with a nifty hesitation move.
Jeff Carter and Mike Richards scored goals in regulation and Sergei Bobrovsky made 28 saves for the Flyers. Philadelphia, with 96 points, breaking a tie with the Washington Capitals atop the Eastern Conference.
Philadelphia went 2-0-1 on its road trip and will return home to meet the Capitals on Tuesday night.
Defensemen Alex Goligoski and Stephane Robidas scored in regulation and Kari Lehtonen stopped 28 shots for the Stars, 2-2-2 in a season-high, seven-game homestand.
Lehtonen fell to 0-10-2 against the Flyers.
Dallas rallied from a two-goal deficit to tie it at 2 at 15:24 of the third period when Robidas skated into the Flyers zone and scored with a slap shot from the slot.
The Stars had a 4-on-3 advantage with 1:37 left in regulation when Kimmo Timonen flipped the puck into the stands on an attempted clearing pass.
But Dallas was unable to cash in on the power play that extended into overtime.
Carter gave the Flyers a 1-0 lead with 1:21 left in the first period when Andrej Meszaros' 40-foot shot deflected off Carter's skate and past Lehtonen.
Richards extended the lead to 2-0 at 1:17 of the second when he flipped a loose puck through Lehtonen's pads from close range.
Goligoski's shot from the blue line beat a screened Bobrovsky at 12:44 of the second to pull the Stars within a goal.
Notes: The Flyers have won straight against the Stars, including a 3-1 victory in Philadelphia on Feb. 5. ... RW Loui Eriksson (upper body) and RW Adam Burish (lower body) were out for Dallas, and D Nicklas Grossman didn't return after sustaining a lower body injury in the first period. Stars LW Steve Ott left the ice early in the third period after he was accidentally hit in the face by a stick, but returned. ... Lehtonen played in his 13th straight game and 59th this season, one more than the previous two injury-plagued seasons.