Hiller was especially busy in the final period when the Hawks outshot the Ducks 19-2, but he held firm, turning aside 39-of-40 shots overall to backstop Anaheim to its third straight win.
With the score tied 1-1 less than 2 minutes into the middle frame, Perry got an open chance during a Blackhawks change, snapping a wrist shot past Corey Crawford for the decisive goal.
Andreas Lilja also scored for Anaheim.
Chicago, losers of three straight, got its only goal from Bryan Bickell. Crawford made 16 saves.