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."
نرشح لكم
بحضور صلاح.. وزير الرياضة يجتمع مع لاعبي منتخب مصر قبل السفر للمغرب
وزارة الأوقاف: إذا لم يجدد الزمالك عقد انتفاع أرض فرع المهندسين سيتم سحبها
إمام عاشور: لا أتعمد الإدعاء.. وإصابتي كادت تبعدني عن كرة القدم
ذا بيست - الكشف عن المصوتين لمحمد صلاح من المدربين وقادة المنتخبات
أبو العينين: هدف منتخب مصر هو الفوز بكأس الأمم الإفريقية
ذا بيست - الكشف عن اختيارات صلاح وحسام حسن للأفضل في العالم
أمم إفريقيا - موعد مباراة مصر الافتتاحية أمام زيمبابوي والقناة الناقلة
منتخب مصر ينهي الاستعداد لكأس الأمم بالفوز على نيجيريا وديا











