Mathew Barzal scored, and Ilya Sorokin made 19 saves for the Islanders (15-10-0), who are 0-5-1 in their past six home games against Nashville.
"I feel like every game could literally go either way when we play Nashville," Barzal said. "That's a good hockey [team] over there. They're heavy and strong, good D, so, yeah, could have gone either way."
Forsberg gave the Predators a 1-0 lead at 14:18 of the first period when he dropped to a knee and one-timed Duchene's feed from the right face-off circle past Sorokin to the near side.
Josi made it 2-0 with a power play goal at 8:22 of the second period with a one-timer from beyond the circles after a pass from Forsberg.
Nashville went 2-for-3 with the man-advantage.
"Our power play was very good," Hynes said.
Barzal was denied by Lankinen on a breakaway at 14:13 but cut it to 2-1 on a power play at 11:06 of the third period with a shot from the left circle.
"He definitely did," Barzal said, when asked if the game could be summarized by Lankinen having a strong game. "Yeah."