Pyramids, who had secured a 2-0 win in the first leg in Kigali on Wednesday, dominated the return fixture to seal their passage comfortably.
Winger Mostafa Ziko opened the scoring three minutes before the break, while midfielder Ahmed Atef doubled the lead with a fine header just before the hour mark.
International fullback Mohamed Hamdy added a third three minutes later, also with a header, to confirm the result.
Strikers Fiston Mayele and Mostafa Fathi squandered several chances that could have widened the margin.
Pyramids FC will face Ethiopia Insurance in the next round on 17 October.
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