Nedeljkovic, who was acquired by the Red Wings from the Hurricanes on July 22, 2021, is 2-1-0 in three starts against his former team with a 2.30 goals-against average and .935 save percentage. His shutout was his third this season and sixth in the NHL.
"Any time you can get a shutout in this League it's always special, so maybe tonight it was a little bit more," Nedeljkovic said.
Moritz Seider, Adam Erne and Filip Zadina scored for the Red Wings (29-35-10), who are 3-1-1 in their past five games.
"I thought our guys battled hard," Detroit coach Jeff Blashill said. "We didn't do everything perfect, obviously. 'Ned' was outstanding. And good for him, by the way. I know this one meant a lot to him."
Antti Raanta made 19 saves for the Hurricanes (48-19-8), who are two points ahead of the New York Rangers for first in the Metropolitan Division.
"We want to finish first," Carolina coach Rod Brind'Amour said. "That's what we set out to do for these 82 games. We still want to accomplish that. It made it a little tough for tonight, but that's still what we're trying to do."