Robert Hagg scored, and Alex Nedeljkovic made 24 saves for the Red Wings (35-36-10), who have lost four straight.
Detroit played without center Dylan Larkin, who was scratched with a lower-body injury.
"I think you're learning about our core, which I'm excited about," Red Wings coach Derek Lalonde said. "I just liked their compete [level] tonight. We're not a very deep team to begin with. Dylan was unavailable for us, we were down 2-0, and I liked their push back against a team like that."
Stefan Noesen gave Carolina a 1-0 lead at 2:46 of the first period. After Kotkaniemi tipped Shayne Gostisbehere's shot from the point, Noesen gathered the puck behind the net and stuffed it inside the left post off Nedeljkovic's right skate.
"I don't know if I loved the first goal against, but it was the perfect storm," Lalonde said. "I thought he gave us a really good chance again. His ability to play the puck against a forechecking team is very valuable."