Hiller, making his first start in nearly a month after battling a lower-body injury, was especially sharp in the first period went he turned away 11 shots as the Pacific Division-leading Ducks racked up their fifth straight win.
Perry's power-play tally 8:44 into the third period gave Anaheim a 3-1 lead while Ryan Getzlaf contributed a goal and an assist in the win.
Peter Holland also found the net for the Ducks.
Sergei Bobrovsky made 26 saves for Columbus.
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