Petr Mrazek allowed three goals on 18 shots before leaving with an undisclosed injury after the second period. He was replaced by Alex Stalock, who made 10 saves.
"[Mrazek] let us know that he wasn't feeling great," Chicago coach Luke Richardson said. "He told me he had a small injury at the end of the second period. He knows his body well because he's had some injuries before. He's an active goaltender. He gave us a heads-up and said he could finish the period.
"[It's] early in the season and, the solid goalie that he is, we took the precaution. I just talked to the trainers and the doctor, and I think he'll have to take tonight to see how it is. Tomorrow we'll make the call and see how he progresses."
Dominik Kubalik had a goal and an assist, and Nedeljkovic made 25 saves for the Red Wings (2-0-2), who extended their point streak to four games.
"There's some will there within our team," Detroit coach Derek Lalonde said. "We'll probably look back at that [third] period. Analytically, it might be one of our better periods as far as chances for and chances against. Obviously, the inability to extend our lead, to get that fourth goal, we had a ton of chances. It's more about not so much extending the lead, but keeping our lead.
"It's painful. We got exactly what we deserved in the third."
Pius Suter gave the Red Wings a 1-0 lead at 9:26 of the first period when Robert Hagg's point shot went in off his skate.
Dylan Larkin extended it to 2-0 on the power play at 10:33, scoring from above the circles with Oskar Sundqvist providing a screen.
Athanasiou cut it to 2-1 on a penalty shot at 5:41 of the second after he was hooked by Filip Hronek on a breakaway. It was Athanasiou's first goal with the Blackhawks after he signed a one-year contract July 13.