The Ducks won for the sixth time in eight games, with their backup goaltender having to make 20 saves. Hiller has allowed two or fewer goals in six of his last seven starts.
Perry scored on a tip-in just 16 seconds into the game and Kunitz added a power-play goal with 47 seconds left in the opening period.
Patrick Sharp gave Chicago its only goal early in the second.
The Blackhawks have lost four straight.
Chicago played for the first time this season without forward Jonathan Toews, who leads all NHL rookies with 15 goals. Toews will be out for a month with a sprained left ankle.