O’Reilly gave the Predators a 1-0 lead at 6:19 of the first period on a wrist shot over the blocker of Shesterkin from the left circle.
Josi gave the Predators a 2-0 lead at 15:52 of the first period with a wrist shot on the power play.
Jacob Trouba cut it to 2-1 31 seconds into the second period when Trocheck found him with a pass from behind the net.
Colton Sissons gave the Predators a 3-1 lead at 7:28 of the second period on a short-handed breakaway. Yakov Trenin chipped the puck off the boards to Sissons, who shot past Shesterkin on the glove side.
Chris Kreider made it 3-2 at 8:52 of the second period on a rebound of his own shot that he batted out of the air off a face-off win as a power play expired.
“I was horrible in the face-off circle tonight (won 10 of 21), and that played a big factor,” O’Reilly said. “On the PK, I’ve got to at least create a 50-50 battle. I can’t be losing them clean like I have been. That could’ve been the difference tonight, and it’s crazy how it comes down to little plays. I’m disappointed in myself. I was awful in the face-off circle tonight.”