Mahmoud Fathalla's goal earned the Cairo outfit a 1-0 first-leg triumph and that proved sufficient to send Mido's men through after an impressive rearguard action in Luanda.
Kabuscorp were somewhat unfortunate in Friday's second leg, having twice seen striker Tresor Mputu spurn good opportunities to break the deadlock.
But the visitors also provided an attacking threat and Moemen Zakareya saw a first-half effort strike the post.
The home side applied concerted pressure in the second half but were denied on several occasions by Zamalek goalkeeper Abdelwahed El-Sayed, who performed admirably between the posts.
And Zamalek were left celebrating at the final whistle as they held firm to deny the Angolan club.
Zamalek now continue their search for a sixth Champions League title, and first since 2002.
