The Ducks had won 13 straight games at home, but they melted away after surrendering four goals in the first two periods.
Jimmy Howard made 33 saves for the Red Wings.
The lone Anaheim goal came from Teemu Selanne in the first period. It was Anaheim's first home loss since Jan. 25. Anaheim will host the Red Wings again on Sunday.
Viktor Fasth started in goal for the Ducks, but was lifted early in the second period after giving up three goals on 11 shots.