Ridly Greig made it 2-0 at 14:19. He took a pass up the middle from Michael Amadio, drove to the net and scored through the five-hole.
Cozens pushed the lead to 3-0 at 10:46 of the second, scoring in the slot with a redirection of a shot by Artem Zub.
“It doesn’t feel good right now,” Cozens said. “That was a big game for us, one we needed to get points out of. We can be [mad] about it tonight, but we’ve got to turn the page. We’ve been playing some good hockey, and there’s a lot of games coming up. We need to find a way to just turn the page and not get too down on it.”
Stamkos cut it to 3-1 at 18:34 with a power-play goal. He scored with a one-timer from the slot off a pass from Evangelista.
Jonathan Marchessault pulled the Predators within 3-2 at 8:19 of the third, finishing a give-and-go with Michael Bunting on a 2-on-0 rush.
Thursday marked Marchessault’s third game back after missing 14 with a lower-body injury.
“I’ve definitely been grinding and trying to get healthy and trying to push through,” Marchessault said. “Today was probably the game that I felt just a little better on my feet. I’m trying to get a little bit more physical, and I’m trying to make the right plays at the right time. But it’s been tough to get healthy this year.”