In a meeting of the teams with two of the three worst records in the Western Conference, the Oilers lost their fifth straight.
Anaheim scored three times in the second period to break things open. Hiller wound up with his 13th shutout in 214 games spread over five seasons.
Jason Blake, who has missed most of the campaign with a wrist injury, opened the scoring with his first goal of the year midway through the opening period.
Nikolai Khabibulin started for Edmonton, but was removed after giving up three goals on 14 shots. The last two Anaheim goals came against Devan Dubnyk.
2014: The Year in Music [PHOTOS]