With the setback, Anaheim dropped to 29-33-12 (70 points) on the season, sixth in the Pacific Division, with eight games remaining on the regular-season schedule.
Troy Terry and Josh Mahura scored for the Ducks. John Gibson made 38 saves in his 51st start of the season.
Staal's hat trick led the Hurricanes offensively, his first three-goal game in nearly a decade (April 8, 2012 with Pittsburgh). Jordan Martinook and Andrei Svechnikov also scored for Carolina. Former Ducks netminder Frederik Anderson stopped 23-of-25 shots to earn his fourth career win against his original NHL team.
Carolina raced out to an early two-goal lead, going ahead just over a minute after the opening puck drop and then adding to the advantage minutes later.
Svechnikov started the scoring with a deflection of Brady Skjei's point shot, lifting a low shot up high over Gibson to give the Canes an early lead. Staal scored his first of the evening shortly thereafter on a centering pass from Nino Niederreiter, quickly getting rid of his shot from the low slot while fighting off checks from two Ducks defenders.
Anaheim answered quickly though, getting right back in the game when Mahura danced away from trouble just inside the Carolina blue line and snuck a wrist shot through traffic in front and past Andersen.