Ville Leino scored in the sixth round of the shootout to give the Flyers their 35th trip to the playoffs.
Claude Giroux had a goal in the second round for the Flyers, but Mike Ribeiro tied it in the third round with a nifty hesitation move.
Leino secured a second point for the Flyers by backhanding a shot into an open net after Kari Lehtonen skated out from the crease to challenge the shooter.
Other than Ribeiro's goal, Sergei Bobrovsky was perfect in the other five shootout rounds.
"In the shootout, he was great and made the saves when he had to," Flyers center Jeff Carter said.
Carter and Mike Richards scored in regulation and Bobrovsky made 28 saves for the Flyers. Philadelphia, with 96 points, broke a tie with the Washington Capitals atop the Eastern Conference.
Defensemen Alex Goligoski and Stephane Robidas scored in regulation and 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.
"Robie didn't get much of a chance but the seas parted and he had a chance to unleash his shot, and it was a great shot. He found a hole," Stars coach Marc Crawford said.
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 five 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 D Karlis Skrastins was done after two periods with an undisclosed injury, leaving Dallas with four defensemen. ... 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.