Hiller stopped all 22 shots he faced in becoming the first goaltender since Pittsburgh's Tom Barrasso in 1992-93 to notch a win in 14 consecutive starts.
Andrew Cogliano got the game's only goal in the second period for the Ducks, who improved to 19-0-2 at home this season and reeled off a 17th victory in 18 games overall.
Petr Mrazek turned aside 22-of-23 shots for the Red Wings, who fell for the fourth time in six contests.
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