Jean-Sebastien Giguere made 13 saves as the Red Wings put the pressure on in the third period as the Ducks held on in Game 6.
Anaheim will play Ottawa in the Stanley Cup finals.
Pavel Datsyuk scored twice for Detroit, which had a 2-1 lead in this best-of-seven series but lost three straight games. Henrik Zetterberg also scored and Dominik Hasek allowed four goals on 29 shots for the Red Wings.
Detroit was trying to reach the title round for the fifth time in the last 12 seasons.
Celebrity Families of 2014 [PHOTOS]