Jesper Fast, Steven Lorentz and Andrei Svechnikov also scored for the Metropolitan Division-leading Hurricanes. They completed a six-game trip by winning four of six.
"It's good to finish the road trip in the right way," Aho said. "Just a great job by our team. Two points. That's huge."
Ivan Provorov, Joel Farabee and Rasmus Ristolainen scored for Philadelphia. The Flyers have lost five in a row.
"Everyone has to be better and that starts with me," Philadelphia coach Alain Vigneault said. "We have to stick together as a group."
The Hurricanes took control by outscoring Philadelphia 4-1 in the second period.
"All our Grade-A's seemed to go in," Carolina coach Rod Brind'Amour.
Aho scored his second of the contest and team-leading 10th of the season 23 seconds into the period to tie it at 2. He raced across the blue line and fired a wrist shot that deflected off Ristolainen's stick and high over goalie Carter Hart.
The Flyers went up 3-2 1:16 into the second on Ristolainen's first since being acquired in the offseason. His hard slap shot beat Antti Raanta on the glove side.
But Carolina answered 29 seconds later when Fast converted a tying goal on a rebound, and the Hurricanes went ahead for good with 5:48 remaining in the second on a beautiful, tic-tac-toe play with Kotkaniemi finishing from close range after passes from Seth Jarvis and Tony DeAngelo.
Lorentz capped the offensive outburst for Carolina, making it 5-3 with 3:38 to play in the second by scoring another pretty Carolina goal from close range.
"We do have some talent, for sure," Brind'Amour said. "But most of them came off doing it right the other way. It was nice to see."
Raanta preserved the two-goal advantage with a stellar pad save on Connor Bunnaman on a 2-on-1 with 2 1/2 minutes left in the period.
"We know we can play better," Flyers captain Claude Giroux said. "We know we can support each other better on the ice. We have to play as a unit of five, and right now we're not.
"As a team, we're flat. We're not playing the best we can and we know that. There's a lot of frustration in our game. We need to reset here and figure it out."
Provorov opened the scoring 50 seconds into the contest. Giroux's pass through the crease went through Philadelphia's Sean Couturier and Carolina's Jordan Staal to the other side, where Provorov was wide open for a wrister. Brind'Amour challenged the goal, saying that Couturier interfered with Raanta, but the officials upheld the goal after video review.
Aho scored his first with a wrist shot from a sharp angle that went over Hart's left shoulder.
"It was a sneaky shot there," Aho said. "Sometimes those go in."
Farabee scored his second in two games and sixth of the season, deking past Seth Jarvis with a fake slap shot and then finishing with a wrist shot through Raanta's legs for a short-handed goal with 2:58 to play in the period that gave Philadelphia a 2-1 lead.
DeAngelo, who grew up a Flyers fan in his hometown of nearby Sewell, New Jersey, had a pair of assists while upping his points streak to four consecutive games.
BLACK FRIDAY GAME
The Flyers continued their tradition of a Friday afternoon game on Black Friday. The contest marked the club's 22nd such contest since 1997, with 20 of those being played in Philadelphia.
Hurricanes: D Ethan Bear (COVID-19 protocol) sat for the third straight contest.
Flyers: C Derrick Brassard (lower body) missed his second straight game. He's likely to miss at least another week. ... C Nate Thompson went down hard in front of the Philadelphia bench with five minutes left in the third and didn't return.
Hurricanes: Host Washington on Sunday.
Flyers: At New Jersey on Sunday.
Carolina's four unanswered goals push them past Philly
The Hurricanes grab a 6-3 road win over the Flyers thanks to four unanswered goals.