The towering striker flicked the ball into the path of central defender Younes Al-Shibani after a corner to help him head the opener after 13 minutes.
He wrapped up the victory himself with 17 minutes remaining via another header to send the home fans into raptures.
Ittihad look favorites to cause a huge upset and eliminate six-time African champions Ahli, who also bowed out of the elite competition at the same stage last season.
But Zuway, whose physical contributions caused Ahli's defense all sorts of problems, is keeping his feet on the ground.
"Nothing is settled yet, the second leg will be difficult. I hope the better team wins," he told Nile Sports after the clash.
Ahli squandered several clear-cut chances when they were 1-0 down and were eventually made to pay for their wastefulness when Zuway capitalized on some slack marking from Wael Gomaa to put the result beyond doubt.
"Our opponents had the better possession but this count for nothing," he added.
"Football is all about scoring goals, and that's what we did tonight. But we still face a tough task in the second leg."
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