Ekman-Larsson launched a shot over the glove of Jonas Hiller, finding the top corner of the net in the tiebreaker, and the Coyotes' Mike Smith made the advantage hold up with a subsequent stop on Bobby Ryan.
Matthew Lombardi provided a goal and assist while Shane Doan, Antoine Vermette and Keith Yandle also scored for Phoenix, which logged its second consecutive shootout win over the Ducks in the middle contest of three straight between the Pacific Division rivals.
Smith finished with 27 saves in the victory.
Ryan Getzlaff tallied with two assists while Corey Perry donated a goal and a helper for division-leading Anaheim.
Hiller turned aside 36-of-40 shots in the setback.