Dan Fritsche and Geoff Platt also scored for Columbus (3-3), which snapped a three-game losing streak. Pascal Leclaire stopped 27 shots.
Justin Williams and Rod Brind'Amour scored for Carolina (0-3). John Grahame made 25 saves.
Williams' shot from the right circle skimmed off Leclaire's glove on the power play to open the scoring at 5:09 of the second period.
Fritsche beat Grahame with a shot from the low slot at 2:27 of the third period to tie the game. Nash scored hits first goal just 1:37 later to make it 2-1.
Brind'Amour tied it at 9:03 of third period, jamming home a rebound for another Hurricanes power-play goal.
Columbus responded 54 seconds later when Platt slid home a centering pass from Alexandre Picard.
Nash capped the scoring with an empty net goal.