Hiller, playing his second NHL season, was busy in the second period when he was peppered by 15 shots.
Normally a backup, he was subbing for Jean-Sebastien Giguere, who returned to his hometown of Montreal for family reasons.
With his ninth this season, Ryan Getzlaf scored the lone goal at 15:19 of the second period after assists by Corey Perry and Bobby Ryan in the Ducks' third straight win following five losses in six games.
Cristobal Huet stopped 20-of-21 shots in the Blackhawks' second straight loss.
Anaheim rose to 13-2 in its last 15 contests against Chicago.
Chicago went 0-for-2 on the power play, while Anaheim was 0-for-1 with the man advantage.
Celebrity Families of 2014 [PHOTOS]