Zegras was second among NHL rookies with 61 points (23 goals, 38 assists) in 75 games last season.
Lukas Dostal made 28 saves for Anaheim. Ryan Strome, who signed a five-year contract with the Ducks on July 13, had a goal and an assist in his debut.
Karel Vejmelka made 20 saves for Arizona.
Pavol Regenda scored his second of the preseason to give the Ducks a 1-0 lead at 17:25 of the first period.
Dylan Guenther tied it 1-1 at 10:18 of the second period, but Strome put Anaheim back in front at 19:06.
Isac Lundestrom pushed the lead to 3-1 at 9:00 of the third period.
