Dallas got a goal and three assists from Valeri Nichushkin, who became the first Stars rookie with four points in a game since Jere Lehtinen did it in 1996.
The line of Seguin, Nichushkin and captain Jamie Benn combined for nine points.
"They came back. Look at all their opportunities in the last game that should have been goals," Stars coach Lindy Ruff said, referencing a 3-2 overtime loss to the Toronto Maple Leafs on Tuesday.
"They came out in the second period and scored right away. We double-shifted them early, and they got it going."
"He played an excellent game," Ruff said of Ellis. "He gave us some real good saves. He's won the last couple. That gives me confidence to keep him in there more often."
Seguin hadn't scored in six games before Saturday and was playing his second after missing two with concussion-like symptoms. His most recent goals came in a 7-3 win at the Calgary Flames on Nov. 14, when he had four.
His first goal Saturday came 39 seconds into the second period when he finished a rush with a snap shot inside the right side of the net to make it 1-1.
After being denied by Flyers goaltender Steve Mason on a breakaway at 9:21 of the second, Seguin connected from the slot at 17:03 after a pass from Goligoski.
With Dallas missing two of its most experienced defensemen, Stephane Robidas (leg fracture) and Trevor Daley (lower body), each injured in the past week, Goligoski led the Stars with 27:31 of ice time, an increased workload he handled well.
"He really has been our best defenseman back there," Ruff said. "With the absence of Robidas and now Daley, we've really loaded up the minutes on him. I admire his bounce-back from sitting out (earlier in the season). You have to give him a lot of credit. He knew he wasn't good enough at the time and came back and wanted to make a difference. He deserves all the credit in the world for that. He's really just taken the ball and run with it."
Seguin's third goal (15th of the season) came 40 seconds after his second when it appeared his wrister was knocked in by Philadelphia's Luke Schenn at 17:43. Dallas scored a third goal in a span of 1:02 at 18:05 when Nichushkin beat Mason with a wrister from the left circle to make it 4-1.
Seguin said his timing was not quite right in the loss to Toronto, but there were no lingering effects against Philadelphia.
"The first practice in Toronto I felt off, and really in the first and second [periods] against the Leafs, I had trouble tracking the puck," he said. "That's because I was coming off a concussion and I hadn't skated really. The third and overtime it felt better last night, and tonight I didn't feel it."
Flyers coach Craig Berube said allowing three unanswered goals in the second period doomed his team.
"Well, I thought that we had trouble with their speed, that one line especially," Berube said. "We didn't do a good enough job with our high forward, and our D had bad gaps, and that's a combination. We let them come at us too much in the second period and it was a problem."
Dallas' Cody Eakin scored a shorthanded goal with 4:33 remaining in the third period.
Philadelphia led 1-0 when defenseman Andrej Meszaros scored his first of the season 1:09 before the first intermission. Wayne Simmonds started the rush for Philadelphia, sending the puck in from the right side. Ellis made a play with his left pad, but with the puck sitting in front of the goal, Meszaros skated and tapped it in.
Mason, who left after two periods for backup Ray Emery, stopped 22 of 26 shots. Emery stopped seven of eight.
"Obviously, there was a minute-and-a-half span where three goals go in," Mason said. "Started off 30 seconds into the period giving up a goal, kind of put us back on our heels, and [we] just were never able to recover after that."
Dallas was unable to score, generating five shots.
"Those guys (penalty kill) killed off seven minutes; great job and we never picked up off it," Berube said.
Dallas was 0-for-5 on the power play, making the Stars an NHL-worst 1-for-42 at home.
"It looked pretty good, but we didn't score again," Ruff said.
Stars center Vernon Fiddler suffered an upper-body injury late in the first period and did not return.
"We'll re-evaluate him on Monday," Ruff said. "Nothing too serious, but he'll miss a little bit of time."
Philadelphia continues its five-game road trip Monday against the Ottawa Senators. Dallas ends a two-game homestand Tuesday against the Chicago Blackhawks.
|Andrej Meszaros (1) ASST: Wayne Simmonds (8), Brayden Schenn (9)|
1 - 0 PHI
|Tyler Seguin (13) ASST: Jamie Benn (19), Valeri Nichushkin (9)|
1 - 1 Tie
|Tyler Seguin (14) ASST: Alex Goligoski (6), Valeri Nichushkin (10)|
2 - 1 DAL
|Tyler Seguin (15) ASST: Valeri Nichushkin (11)|
3 - 1 DAL
|Valeri Nichushkin (4) ASST: Tyler Seguin (12), Alex Goligoski (7)|
4 - 1 DAL
|SHG - Cody Eakin (7) ASST: Antoine Roussel (6)|
5 - 1 DAL
|Zac Rinaldo Fighting (maj) against Antoine Roussel|
|Zac Rinaldo Instigator against Antoine Roussel|
|Zac Rinaldo Misconduct (10 min) against Antoine Roussel|
|Zac Rinaldo Game misconduct against Antoine Roussel|
|Ryan Garbutt Boarding against Nicklas Grossmann|
|Michael Raffl Tripping against Jamie Benn|
|Kimmo Timonen Hooking against Jamie Benn|
|Jordie Benn Interference against Wayne Simmonds|
|Jordie Benn Elbowing against Michael Raffl|
|Brenden Dillon Roughing against Sean Couturier|
|Sean Couturier Roughing against Brenden Dillon|
|Sean Couturier Misconduct (10 min) against Brenden Dillon|
|Brenden Dillon Misconduct (10 min) against Sean Couturier|
|Tyler Seguin Hooking against Andrej Meszaros|
|Wayne Simmonds Roughing against Jordie Benn|