Aho added his first goal of the season and two assists, and Jordan Staal‘s career-best four assists gave him 201 with the Hurricanes. Jeff Skinner scored the other Carolina goal in the closing seconds.
Scott Darling stopped 25 shots for the victory.
"I liked the fact we scored on the power play," Carolina coach Bill Peters said. "That gave us momentum. It gave us life. It was good for (Aho) to get one. The guys were happy for him. I don’t know who was happier for him, collectively the team on the bench or himself."
Alexander Radulov scored for Dallas, which won the previous meeting at home 4-3 on Oct. 20. The Stars came out on top in their previous three trips to Raleigh.
"It’s disappointing," Dallas coach Ken Hitchcock said. "We had the game right there and we cracked. We were in a great position on the road, exactly where we wanted to be, and we were the ones who made the mistakes."
Aho’s first goal came in his 14th game of the season, two earlier than last season when he finished with 24 goals.
Carolina took the lead on a rush at 8:07 of the first period as Aho beat Ben Bishop through the legs after Staal’s pinpoint centring pass from the left wing.
Radulov tied it by working hard in the slot on a power play at 8:44 of the second.
But the Hurricanes went ahead again on a power play at 2:39 of the third, with Teravainen scoring on a rocket from the left point. Staal and Aho had assists on Carolina’s first power-play goal this month.
"My goal came on a great play by Teuvo," Aho said. "Then Jordan made a great (centring) pass and I finally got my first one. That felt pretty good. Teuvo was on fire and it was fun to play with him today. Jordan was good. It was a lot of fun playing with both those guys today."
Teravainen made it 3-1 at 6:51 from the high slot, getting the puck past Bishop with Aho providing a screen.
"It’s been a struggle with the power play lately and I haven’t been scoring that many goals," said Teravainen, who has six on the season. "I just go out and play and try to do my thing, and sometimes the puck goes in. It was exciting when (Aho) finally scored a goal, and I felt good for him. I guess his luck is going to turn around."
Bishop finished with 23 saves.
NOTES: Dallas D Marc Methot missed his second straight game with a lower-body injury. … Carolina RW Lee Stempniak (upper body) was placed on injured reserve after getting hurt Friday during his AHL conditioning stint. … LW Phillip DiGiuseppe and D Klas Dahlbeck were healthy scratches for Carolina. … Dallas’ healthy scratches were C Jason Dickinson and LW Remi Ehle.
Stars: At the Florida Panthers on Tuesday night, the second stop on a three-game road trip.
Hurricanes: Visit the New York Islanders on Thursday night.