Zamalek have been in poor form domestically and sit eighth in Group 2 of the Egyptian top flight.
They held Zambia's Nkana to a goalless draw in the first leg of their tie earlier this month, though, and ran out 5-0 winners in Sunday's meeting.
Ahmed Tawfik netted the opener after 20 minutes and Mo'men Zakaria also scored before the break.
Omar Gaber's effort, two minutes after the resumption, effectively sealed the result but there was still time for Hazem Emam and Ahmed Gaafar to get their names on the scoresheet.
Haythem Jouini's first-half goal settled nerves before Iheb Msekni and Harrison Afful found the net to complete a routine win.
Algeria's ES Setif won 1-0 at Cameroon's Cotonsport to progress 2-0 on aggregate, while Sudan's Al Hilal and Leopards de Dolisie drew 0-0 in Sunday's other clash.
