Morgan Geekie scored again for Carolina (38-25-5), which has won three in a row and is tied with the Columbus Blue Jackets for the first wild card, one point ahead of the New York Islanders.
"That was a game where you look at the standings and you expect to win, but you still have to respect the game," Hurricanes forward Justin Williams said. "We still had to go out there and work against a scrappy team that's fighting against you."
WATCH: [All Hurricanes vs. Red Wings highlights]
Petr Mrazek made 23 saves in his return after missing the previous six games because of a concussion/neck injury.
"You could tell he was going to be solid right from the start," Hurricanes coach Rod Brind'Amour said. "That's what we needed from him, plus he added some really big saves."
Jonathan Bernier made 31 saves for Detroit (17-49-5), which had won two straight but is 3-10-1 in its past 14 games. The Red Wings allowed three goals on specials teams in the third period, two to the Hurricanes power play and one shorthanded.
"I thought we played fairly well for 40 minutes, but the specialty teams obviously weren't good enough in the third period," Red Wings coach Jeff Blashill said. "That's the difference in the game."
Geekie gave the Hurricanes a 1-0 lead at 8:58 of the first period on a give-and-go with Warren Foegele. Geekie has three goals in his first two NHL games since being called up March 7.
"He's obviously got some skills and he has a lot of confidence," Brind'Amour said. "He's just going out there and ripping the puck."