Carter snapped a tie when his shot bounced through the legs of goalie Craig Anderson. Darroll Powe added an empty-netter only moments later for some insurance on the night the Flyers raised their Eastern Conference champions banner.
Claude Giroux scored a short-handed goal for the Flyers. Rookie goalie Sergei Bobrovsky had another solid game for the Flyers.
Brandon Yip and Milan Hejduk scored for the Avalanche to help them rally from a 2-0 hole and tie the game.
Chris Pronger returned to Philadelphia's lineup after missing the first two games as he recovered from offseason knee surgery. Pronger, one of the NHL's top defenseman, said during the second intermission his timing was off and that he needed about a week to "get back on track."
Carter got the Flyers back on track late in the game after they blew an early 2-0 lead. Mike Richards set up the winner with a nice pass and Carter knocked the puck off the inside of Anderson's leg and through them for a 3-2 lead.
That helped make the Flyers and their fans as happy at the end of the game as they were at the start.
The Flyers held a lengthy pregame tribute to their stunning run to the Stanley Cup finals. All the big goals and the historic 3-0 comeback against Boston were highlighted before the opening faceoff.
Pronger, Richards and coach Peter Laviolette all heard rousing ovations, but the loudest one was saved for injured forward Ian Laperriere. His career is likely over as he suffers from the lingering effects of post-concussion syndrome. Laperriere was hit by a puck blocking a shot late last season and fought his way back to the lineup. His valiant effort was certainly not forgotten by Flyers fans.
The crowd went wild when the Flyers unfurled their Eastern Conference champions banner.
It's nice addition to the rafters - it's just not the championship banner the Flyers wanted.
The fans kept roaring well into the first period after Giroux and Carter put them up 2-0.
Giroux struck first on his second short-handed goal already this season, this one a backhand against Anderson with 7:31 left in the first. Carter made it 2-0 when he beat Anderson on almost the identical type of backhand goal.
The lead didn't stick. Yip added a goal in the second period and Hejduk tied it only 32 seconds into the third. His soft shot trickled through Bobrovsky's legs for the easy score.
Notes: Flyers G Michael Leighton had back surgery on Monday. He will begin his rehabilitation this week and is expected to make a full recovery. The Flyers had already said Leighton would miss six to eight weeks. ... The Avalanche beat the Stanley Cup champions in their opener. Now, they've lost to the runner-ups.