Anthony Duclair gave the Panthers a 1-0 lead at 5:02 of the second period, beating Nedeljkovic with a one-timer off Barkov's rink-wide pass.
Sam Reinhart made it 2-0 at 6:32 off a pass from Mason Marchment.
Florida took a 3-0 lead at 14:23 when Lundell scored on a rebound after a turnover by Detroit defenseman Jake Walman, and Maxim Mamin made it 4-0 at 14:51.
"We felt like the chances were pretty even after two periods, but they scored on theirs and we didn't score on ours," Red Wings coach Jeff Blashill said. "Against that team, you pretty much have to be perfect, and we weren't, so it's 4-0."
Lundell scored shorthanded for a 5-1 lead at 5:04 of the third period, converting Barkov's drop pass between his legs.
"I was just trying to keep up with him," Lundell said. "But he obviously has eyes in the back of his head because he put that puck right on my stick."