Brock McGinn scored twice, and Nedeljkovic made 39 saves for the Hurricanes, the No. 1 seed.
"I thought we played great," Carolina coach Rod Brind'Amour said. "Felt like we had the play most of the game. In overtime, it felt like we were at their end. Eventually, they're going to score if we don't score. We couldn't find a way to get one, but I love the way our guys are playing."
Game 5 of the best-of-7 series will be at Carolina on Tuesday.
"It's definitely draining, disappointing losing those two," McGinn said. "But they're playing just as long as we are. We're both in the same situation. Everyone has to go home, we have to recover, regroup and come back the day after."
Kunin scored 57 seconds into the first period to give Nashville a 1-0 lead. Granlund tried to split Brett Pesce and Brady Skjei, and the loose puck went to Kunin, who shot five-hole on Nedeljkovic while cutting through the low slot.
Vincent Trocheck tied it 1-1 at 18:03. Martin Necas toe-dragged Matt Benning before fanning on a shot, but the puck trickled into the crease, where Trocheck swiped it into the net.
Ryan Johansen gave the Predators a 2-1 lead at 4:53 of the second, scoring on a backhand in the slot after Nedeljkovic failed to cover a loose puck.
"We did a lot of good things tonight," Johansen said. "You've just got to be mentally tough. You've got to stay ultra-focused, and your details got to be very sharp."