Goaltender Jonathan Bernier turned aside 29 shots and the Red Wings blocked 17 shots on the night, including 10 saves in the first period.
Thursday's contest marked the fourth straight game the Red Wings only had one power-play opportunity (0-for-1). Detroit held Carolina's league-best power play to 0-for-3 on the night.
The Red Wings outshot the Hurricanes, 8-6, in the opening frame before Carolina's offense found its footing, outshoot Detroit, 26-9, in the final two periods.
Detroit had the first scoring chance three minutes into the game when forward Michael Rasmussen sprung loose on a 2-on-1 odd-man rush and sent a perfect backhand pass to Vrana, who pulled the puck to his backhand and hit the crossbar.
Carolina had its best opportunity of the period eight minutes into the frame when forward Vincent Trocheck received a perfect backdoor pass at the top of the crease. Trocheck fired a quick shot, but Bernier got a piece of the puck with his glove to keep it out.