The Ducks boosted the NHL's largest point total to 29, bouncing back from a loss to Los Angeles on Monday that ended their six-game winning streak.
Anaheim already had a 1-0 lead when Palmieri scored his first goal of the game and the Ducks' second in a span of 61 seconds. He tallied again with 3:03 to go in the opening period and then produced a power-play goal 1:07 into the middle stanza.
The other Anaheim goals came from Nick Bonino and Saku Koivu.
Nashville managed only a second-period goal by Craig Smith against Viktor Fasth, who made 20 saves while improving to 9-1 for the season.
Pekka Rinnie gave up five goals on 16 shots before being removed in favor of Chris Mason.