Ilya Sorokin made 37 saves for the Islanders (7-12-5), who had won two of three following an 11-game losing stretch (0-8-3).
Nedeljkovic came within 2:33 of a shutout before Anders Lee tipped in a point shot with Sorokin pulled for the 2-1 final.
"I think there was just too many lapses in our own end that gave them some opportunities to keep momentum," Lee said. " … We ended up chasing for too much of the game tonight. The third period was a lot better, but we've got to find a way to be like that all 60 (minutes)."
New York nearly scored first at 3:15 of the second period, but Anthony Beauvillier missed an open net with Nedeljkovic out of position.
Larkin ended a seven-game goal drought at 10:32 with a point shot that went off Sorokin's blocker for a power-play goal to give the Red Wings a 1-0 lead.
The Islanders used their timeout at 13:05 of the second period before Nedeljkovic had to make a save against Beauvillier on a 3-on-1 break at 19:37, and Robin Salo hit the post five seconds later.
"We had played a great second period and then we made one mistake right at the end," Blashill said. "Luckily, Alex made the save, because it would have been really tough to give one up in the last few seconds."