Jon Merrill scored with a backhand from the slot at 14:35 to make it 2-0 after William Carrier brought the puck into the Carolina zone on the left side, skated it behind the net, and passed to the defenseman in the right face-off circle.
Teuvo Teravainen, playing in his 300th game in the NHL, scored with a wrist shot through traffic from the right point to make it 2-1 with 29 seconds left in the first.
Theodore scored for the second consecutive game to give the Golden Knights a 3-1 lead 59 seconds into the second.
Aho scored for the sixth time during his streak to get the Hurricanes within 3-2 at 1:19 of the third, but Chandler Stephenson scored shorthanded at 2:17 to make it 4-2.
Haula scored on the power play to make it 4-3 at 4:16.
Haydn Fleury tied it 4-4 at 10:48. The goal initially was disallowed for goaltender interference, but Hurricanes coach Rod Brind'Amour challenged, and the call was overturned after video review.
"They pushed, and we turned pucks over and took some penalties," DeBoer said. "Some uncharacteristic things. We've been playing some real solid hockey for a while, and the second and third, I thought, we were our own worst enemy."