Zegras earned the Ducks the extra standings point in overtime, finishing off a remarkable setup effort by John Klingberg, who finished with two assists. Max Jones also scored for Anaheim.
John Gibson earned his tenth win of the season, his third in his last four starts, stopping 32-of-33 Arizona shots, including a truly jaw-dropping game-saving stop in overtime that kept the Ducks alive.
Anaheim fired 45 shots on net in the win, the club's best total of the season.
Nick Ritchie scored the lone goal for the Coyotes, who fell to 16-28-6 on the season and 6-20-4 on the road. Netminder Connor Ingram made 43 saves in a hard-luck loss after keeping Arizona in the game early.
Anaheim controlled much of the first period territorially, but it would be Arizona that returned to the locker room with an early lead despite an 16-10 Ducks edge in shots.
The Ducks nearly found the night's first goal on several occasions early, first on a mad scramble in front of the Coyotes net that had the whole building holding its breath. Anaheim then kept up the pressure throughout a subsequent power play, with Grade-A looks coming in tight by McTavish and moments later on a one-timer by Silfverberg.
Instead Arizona would go ahead first, with an old friend delivering the opening salvo. Two minutes after his roughing penalty expired, Ritchie held a puck in at the Anaheim blue line, sweeping it back into the zone for Christian Fischer behind the net. Fischer then stepped out in front and returned the favor to Ritchie, sliding a cross-seam pass that Ritchie lifted home before his former teammate Gibson could slide across.
Ritchie, selected 10th overall by Anaheim in 2014, has three points in his last two games (1-2=3) and 9-12=21 points in 47 games this season.
The former Duck nearly added to the Arizona advantage in the middle frame, getting inside positoning in the low slot and coming inches from shoveling home a rebound from the side of the net, but Gibson stretched across to get just enough with the left pad to keep it a one-goal game.