It was the third career shutout for Annunen and first in 84 starts since he recorded back-to-back 5-0 wins against the Chicago Blackhawks on Feb. 29 and March 4, 2024, while playing for the Colorado Avalanche.
Erik Haula had a goal and an assist, and Ryan O'Reilly and Joakim Kemell each had two assists for Nashville (37-31-10), which was coming off a 3-2 shootout loss at the Los Angeles Kings on Monday.
With the win, the Predators moved one point ahead of the Kings for the second wild-card spot in the Stanley Cup Playoffs from the Western Conference.
Lukas Dostal made 20 saves for the Ducks (41-32-5), who have lost six in a row (0-5-1). Anaheim dropped to third place in the Pacific Division, a point behind the Edmonton Oilers and Vegas Golden Knights, who each have 88 points.
Nashville was getting outshot 20-9 when Kemell faked a shot before pulling up above the right circle. He fed Haula cutting down the middle and he scored with a wrist shot over Dostal's blocker for a 1-0 lead at 7:07 of the second period.
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.
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.