With help from a screen in front of the net by Jordan Staal, Aho scored on the power play with a slap shot from inside the blue line to put the Hurricanes ahead 5-4 at 7:17 of the third period.
Taylor Hall, Logan Stankoven, and Seth Jarvis each had a goal and an assist, and Brandon Bussi made 24 saves for the Hurricanes (37-15-6), who have won four in a row and extended their point streak to 11 games (9-0-2).
Bussi improved to 24-3-1 in his first NHL season.
Brayden Point had a goal and an assist, Jake Guentzel had three assists, and Jonas Johansson made 28 saves for the Lightning (38-15-4), whose six-game winning streak ended.
Carolina took a 1-0 lead at 1:43 of the first period thanks to Nikolaj Ehlers, who took a stretch pass from K’Andre Miller in the neutral zone before scoring from the right face-off circle on a snap shot that beat Johansson stick side.
Stankoven pushed the lead to 2-0 at 2:56. After he gathered a loose puck near center ice, Stankoven passed to Hall and got the return pass for a redirect at the right post.
Hall scored on a tap-in at the left post to make it 3-0 at 6:41. Jackson Blake took a pass from Stankoven, then stick-handled around a diving Lightning defenseman Darren Raddysh into the slot before connecting with Hall.
Brandon Hagel cut the lead to 3-1 at 16:30 when he got a snap shot off from the left circle thanks to a pass from Scott Sabourin behind the goal line.
Just 35 seconds later, the Lightning made it 3-2 at 17:05 when Kucherov took a backhand pass from Point in the right circle and held the puck briefly before scoring on a snap shot under the crossbar. The goal extends Kucherov's point streak to 12 games.
Dominic James tied it 3-3 at 1:58 of the second period. Guentzel’s touch pass from along the boards set up James, who skated past Miller and scored on a shot over Bussi’s right pad.
Carolina took a 4-3 lead at 7:21 when Jarvis took a backhand pass along the goal line from Andrei Svechnikov and scored glove side from the left hash marks.
Six seconds into a power play, Point scored to tie it 4-4 at 14:02. His snap shot from the right hash marks came off another touch pass from Guentzel along the goal line.