Nick Bonino and Saku Koivu also scored for Anaheim. Corey Perry and Ryan Getzlaf assisted on all three goals by Palmieri, who hadn't scored since netting back-to-back game-winners on Feb. 1-2 against Minnesota and Los Angeles.
Palmieri completed his outburst against Pekka Rinne 1:07 into the second period, during a power play after Nashville had too many men on the ice.
It was the sixth natural hat trick in club history and marked the third career multigoal game for the 22-year-old forward, selected by the Ducks in the first round of the 2009 draft.
Anaheim (14-3-1) tied Montreal for the second-most points in the NHL behind Chicago's 35. The Ducks have won seven of eight overall.
Rinne gave up five goals on 21 shots before he was replaced at the start of the third period, and Craig Smith scored Nashville's goal.
Rinne allowed at least four goals for the third game in a row after coming in with a 1.90 goals-against average and a league-best three shutouts. Rinne was 7-0-2 with a 1.58 GAA in his previous nine starts against Anaheim—both losses coming this season in shootouts.
The Predators fell behind 2-0 before getting their first shot at 6:11 of the first period.
Anaheim's first goal came on a simple dump-in play, as Rinne mishandled the puck behind the net. Rookie Emerson Etem, recalled from the minors on Tuesday, came in hard and fed a pass in front to Bonino, who scored his fifth goal of the season at 2:48.
Palmieri finished off a 2-on-2 rush with Perry 61 seconds later, getting a pass in the left circle and swerving around Predators captain Shea Weber before cutting in front of the crease and jamming the puck past Rinne's outstretched left leg at 3:49.
Palmieri connected again at 16:57 of the first, converting Perry's pass from behind the net after Getzlaf won a faceoff in the Nashville zone.
NOTES: The first-period goals by Bonino and Palmieri gave Anaheim nine players with five or more, the most of any team. ... Palmieri is the second-youngest player to get a hat trick for the Ducks. The youngest was Bobby Ryan, who did it at age 21 on Jan. 8, 2009, in Los Angeles. ... The Ducks' home winning streak is their longest since a club-record 11-game stretch in the 2009-10 season. ... The Ducks were 11-2 in February, tying the franchise record for wins in a month. ... The Predators were 0 for 10 on the power play during the Ducks' three-game, season-series sweep. ... Palmieri's final goal ended a run of 15 unsuccessful power plays by the Ducks against Nashville in the regular season. ... Anaheim C Daniel Winnik, the first player in franchise history with five goals in the first four games, hasn't scored in 14 games since. ... The Ducks are 8 for 14 on the power play in their last four games.