The Ducks produced four shootout goals to fight off the Coyotes, who surrendered a late lead en route to their second straight loss.
Nick Bonino produced the tying goal for Anaheim with just 2:02 left in regulation, the first score the Ducks had managed since Teemu Selanne tallied 6:38 into the game.
Both Bonino and Selanne scored during the shootout as well, but it was Silfverberg who put the game-winner past Mike Smith.
Hiller finished with 30 saves and earned the victory despite allowing three goals in the shootout. Smith stopped 37 shots.
Anaheim has not lost since a season opening setback at the hands of Colorado.