The Pens unleashed 21 shots Carolina's Justin Peters in the second period but scored just once when Neal got his 12st goal of the season midway through the frame to even the score at 1-1.
Pittsburgh then broke the game open with three goals within the first 8 minutes of the final frame.
Marc-Andre Fleury turned aside 16-of-18 shots as Pittsburgh won its fourth straight contest.
Tim Brent and Tuomo Ruutu scored and Peters finished with 48 saves for the Hurricanes.
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