The Predators were on their first power play when Filip Forsberg scored with a wrist shot from above the circle with O'Reilly providing a screen to make it 2-0 at 11:26.
The Predators killed a 22-second 5-on-3 power play late in the second period and then scored short-handed on the second penalty when Brady Skjei finished a 2-on-0 breakaway for a 3-0 lead at 19:00.
Zachary L'Heureux scored from in front of the crease to finish off a rush and extend the lead to 4-0 at 9:51 of the third period.
“We’ve got to stop giving them odd-man rushes," Killorn said. "We give them a short-handed goal. Just a lot of breakaways and stuff like that. Shot-wise, I feel like we're doing a good job producing shot volume, but we haven't been able to score.”
Fedor Svechkov redirected a centering pass from in front of the crease to make it 5-0 at 15:07.
Nashville killed another 5-on-3 that lasted 1:26 late in the third period and finished 6-for-6 on the penalty kill.
"We hung in there," Brunette said. "I thought 'Big Juice' was outstanding, especially early in the first. Back-to-back (games), we had a little trouble getting going a little bit. Didn't think we found our game until the second (period). That and the penalty killing kind of won us the game tonight."
The Ducks had the only two power plays of the scoreless first period and outshot the Predators 12-5.
Anaheim's best scoring chance in the opening period came on a breakaway by Troy Terry, but Annunen made the save with six seconds left.
"It's always easier when you get shots early and get a lot of shots," said Annunen, who finished one save short of his NHL career high.
NOTES: Forsberg extended his point streak to five games (five goals, three assists). ... Anaheim used 10 forwards and eight defensemen. ... Ducks forward Mason McTavish played in his 300th NHL game. ... Anaheim defenseman Pavel Mintyukov, who missed the previous three games with a lower-body injury, played in his 200th NHL game.