Ahmed Eid and Hazem Emam gave Zamalek a two-goal cushion in the first half before Ahmed Gaafar and newly-signed striker Ahmed Ali completed the rout on his debut.
The match also saw another summer-signing in Momen Zakaria, who joined on loan from ENPPI, make his full debut but was replaced in the second half.
Twenty-one-cup champions Zamalek now meet Military Production in the quarter-finals.
Eid gave Zamalek the lead after 21 minutes after slotting home a loose ball inside the area following Shikabala's cross.
Eight minutes later, Emam doubled his side's advantage through a wonderful goal with the outside of his boot after being brilliantly set up by Shikabala.
Shikabala's exploits continued as he released Emam again down the right but the latter this time crossed for Gaafar who nodded home on the hour mark.
Egypt international Ali, who came on as a second-half sub, opened his Zamalek account from the spot after Mohamed Ibrahim had been pulled inside the area, securing a comprehensive win for the Cairo giants.
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