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Sebastian Aho scored for the Hurricanes (24-20-8), who lost for the first time in four games.
With Detroit leading 3-1 and Helm about to exit the penalty box, Luke Glendening blocked a shot by Carolina forward Teuvo Teravainen. Helm got to the loose puck in the neutral zone, and then beat goalie Scott Darling with a slap shot from the low slot at 13:48 to make it 4-1.
"I think I made that move because I've struggled putting the puck in the net by making moves," said Helm, who ended a 15-game goal drought dating to Dec. 5. "I dumbed it down a little bit, and it worked out."
The Hurricanes had two shots on goal and Justin Faulk hit the post with Helm in the penalty box.
"Would have been nice to get one there," coach Bill Peters said. "I don't think it was the turning point in the game, to be honest with you. We could have been a little more diligent throughout the game, from the first period on."