The 6-foot-4 Heeter, promoted from the AHL's Phantoms for the game, allowed a goal on the first NHL shot he faced, then surrendered a pair of softies later in the first period. Carolina scored three times on its first nine shots.
Heeter (33 saves) steadied himself after the shaky start - the former Ohio State star received several Bronx cheers after making some easy early saves - but Jeff Skinner (two goals) gave Carolina a 5-4 lead when he scored on a rebound with 4 minutes, 21 seconds left in the game. The play developed after a crazy carom off the back boards and a great initial stop by Heeter.
"It took me a while to settle down and feel comfortable out there," Heeter said. "About halfway through the game, I started to settle down."
Wayne Simmonds sent the game into overtime by scoring with 9.5 seconds left. Simmonds (two goals) finished with a career-high and team-best 29 goals - one more than Claude Giroux, whose 86 points put him No. 3 in the NHL.
Kimmo Timonen, who is contemplating retirement after the playoffs, scored a power-play goal in what may have been the final regular-season game of his superb 15-year career.
Sean Couturier equaled a career high with a second-period goal, his 13th, as the Flyers overcame a 4-1 deficit.
The Flyers, who finished with a 3-8 shootout record this season, rested many of their regulars, including Andrew MacDonald, Nick Grossmann and Michael Raffl.
The Flyers insist they are not putting pressure on defenseman Shayne Gostisbehere to sign.
"It'll come down to Shayne and when he thinks the time is right," said Chris Pryor, the Flyers' scouting director.
Gostisbehere had a goal, two assists and a plus-7 rating, leading Union to the NCAA title with a 7-4 upset win over Minnesota at the Wells Fargo Center on Saturday.
"He rose to the occasion, and it was exciting for us to watch, exciting for the kid, and obviously exciting for Union," Pryor said. "He's got some ability that separates him from his peer group. We're excited about his ability."
If Gostisbehere does sign, he probably won't compete for a job with the Flyers next season.
"In a perfect world, you don't want to rush things," Pryor said. "It would come down to the kid and how he progresses in the summer. I don't think there's any rush here. You have to have patience."
Told that some fans, excited by Gostisbehere's Frozen Four performance, think he could help the Flyers next season, Pryor said, "I think everybody has to temper that a bit. We all know he has a lot of talent, but going from college to pro is a big jump. Going to the American League is a big jump, and I think he's aware of that."
The Flyers handed out several awards before the game:
Bobby Clarke Trophy (MVP): Giroux; Barry Ashbee Trophy (best defenseman): Timonen; Pelle Lindbergh Memorial Trophy (most improved player): Raffl; Yanick Dupre Class Guy Memorial Award: Jake Voracek; Gene Hart Memorial Award (fan club award to the player who shows the most heart): Mason.