Mike Smith stopped 35 of 39 shots in the win, returning to the lineup after missing two games and two periods of another.
Brandon Manning, Sean Couturier, Ivan Provorov, and Nolan Patrick answered for the Flyers.
Brian Elliott, playing his first game against the Flames since leaving the team, stopped 26 of 31 shots.
"When guys step up and do little things, it means a lot to the guys on the bench," Monahan said. "So I think tonight was a big win, Smitty stood on his head again like always, and we're leaving here with two points that we came for."
It was the Flyers who opened the scoring early when just 92 seconds in when Manning's shot from the blue line went up, off of Smith's shoulder, off the post, off of Smith's back, and in.
But Gaudreau, who grew up just outside of Philadelphia, answered in beautiful fashion. Showing off in front of family and friends, he received a pass from Micheal Ferland, and was off to the races, bearing down on Elliott on a breakaway. He made no mistake, shooting it in between Elliott's pad and blocker short-side to tie the game.
The Flyers got the lead back, though, on the powerplay. Jakub Voracek's shot led to a rebound Smith couldn't corral, and Couturier was there to roof the puck right over him.
Shortly after, Provorov gave the Flyers a multi-goal lead with a seeing-eye shot from the top of the circle, over Smith's shoulder and in.
"I felt better as the game went on," Smith said. "The first few goals were just kind of crazy ones that found their way in.
"Fortunately I was able to get back in there and kind of get some momentum as the game went on and felt like I was solid from then on in."
The Flames - and Monahan, specifically - came back with a vengeance in the second period, scoring three powerplay goals.
"He's got a great shot," Gaudreau said of his longtime linemate. "Makes my job pretty easy, I just find him in the slot, and he's got a world class shot there. I always give him a hard time, he hasn't had a hat-trick, he's got like 100-something goals, and he got his first one tonight. So really happy for him, he deserves it, and he played well tonight."