Gionta scored to make it 4-3 at 14:10 of the third period. Girgensons made a cross-ice pass to Gionta, who beat Saros for his 11th goal.
Arvidsson gave the Predators a 3-2 lead at 5:08 of the third period on the power play. Arvidsson got to the rebound of his own shot and jammed the puck past Lehner for his 12th goal.
Neal gave the Predators a 4-2 lead at 10:17 of the third period on a one-timer from the slot. Forward Calle Jarnkrok led the rush and fed Neal with the pass, and he shot it past Lehner for his 17th goal.
Forsberg gave the Predators a 1-0 lead at 8:43 of the first period on a shorthanded goal. It was his 15th goal of the season and his 12th in his past 18 games.
Girgensons tied the game 1-1 at 12:12 of the second period on a rebound.
McLeod gave the Predators a 2-1 lead at 17:28 of the second period on an attempt from behind the net for his third goal.
"There was a few shifts where we were stringing some good [offensive zone] time together, and then a couple lapses," McLeod said. "[We] couldn't get the puck out of our end, and that's what happens. It's in the back of your net."
Eichel tied the game 2-2 with 17.4 seconds remaining in the second period.