Gaudreau, who had two assists, scored on the rebound of a Giordano shot to give Calgary its NHL-leading seventh win when trailing entering the third period.
The Flames and Pittsburgh Penguins are the only NHL teams this season to win three games they trailed by multiple goals in the final two minutes.
"It took all 60 minutes, but it was a good effort in the third," said Gaudreau, who has 23 points (seven goals, 16 assists) in the past 13 games. "We didn't play our best hockey in the first and second, but we stuck with it and found a way to play a little bit harder in the third and get the two points."
The Flyers were 5-for-6 on the penalty kill, including 4-for-4 in the third period.
"They gain momentum even if we kill them off," said Couturier, who played 26:16 after missing the previous two games with a lower-body injury. "They gained momentum. Late in the third, 6-on-5, we've got to be better. We kind of let them set up. It's too easy out there. That's what happens. They're good players. They have a lot of talent and a lot of skill, and if you give them time and space, they make you pay."
Bennett put the Flames up 1-0 at 9:13 of the first period when he scored on the rebound of Tkachuk's wraparound attempt.