Hiller, who has not played since being pulled during a February 2 game when he allowed three goals on 10 shots, needed just 12 saves against Edmonton as Anaheim (32-21-4) moved into a tie with the Dallas Stars for top spot in the Pacific Division.
Anaheim have now beaten the Oilers in eight of nine games stretching back to early 2009.
"I thought they had a couple of good opportunities," Hiller told reporters. "Most of the shots they had were odd-man rushes and back-door plays.
"I thought I had a couple of good saves at the right moments."
Anaheim got off to a fast start when Teemu Selanne opened the scoring 34 seconds into the first period. Brandon McMillan and Bobby Ryan scored in the second and Ryan added another when he tallied with just 91 seconds to play.
For the last-place Oilers (16-32-8), the loss was their 12th in their last 14 games.
Edmonton managed just five shots in the first period, four in the second and three in the third.
"I just think we have to challenge ourselves to be a lot better," Oilers' winger Taylor Hall said.
"I truly believe everyone in this room cares and everyone is giving it their all, but at some point this has to turn into results."
(Writing by Jahmal Corner in Los Angeles; Editing by Frank Pingue/Greg Stutchbury)