Lukas Dostal stopped 26-of-28 Arizona shots in his second start of the season.
Jason Zucker and Clayton Keller scored for the Coyotes, who improved to 3-2-0. Karel Vejmelka earned the win in net with 32 saves.
Arizona took the lead late in the first period on the second of consecutive power plays. With Leo Carlsson sitting for interference, Zucker's one-timer from the right circle hit Jackson LaCombe on the way and changed direction enough to sneak by Dostal inside the near post.
The second period was largely controlled by the Ducks, as Anaheim directed 17 shots on net, but the only goal of the frame came off the stick of Keller, who picked his corner past a screened Dostal with the extra attacker on for a delayed penalty.
The Ducks would finally break through early in the third with a power-play goal of their own when Silfverberg set up Vatrano with a backdoor chance off the rush.