Bassem Morsy, whose strike settled the first-leg clash in Port Harcourt, struck again from the spot to hand secure a knockout berth for Mohammed Helmy’s side.
The People’s Elephant, desperate for their first points of the competition, were solid defensively as keeper Theophilus Afelokhai stood firm in the opening 15 minutes against the rampaging attack of Zamalek.
Then in a rare foray forward, Ifeanyi Onuigbo was picked out in the 18th minute but his header was turned out for a corner by Ahmed El-Shennawi in goal for Zamalek.
Mostafa Fathi came close for the hosts five minutes from the break, but his effort was blocked by Emma Anyanwu to leave the game goalless at the interval.
Paul Aigbogun’s men than conceded a cheap penalty shortly after the hour mark as defender Chinedu Udoji was adjudged to have handled Ayman Hefny’s shot.
Morsy did not need a second invitation as he beat Afelokhai from the spot to put the hosts in front in the 63rd minute.
Zamalek ramped up the pressure, with Abdullah Fathi losing his markers five minutes later but firing wide from close range.
Chima Akas came close for the visitors in the 74th minute when his long range effort crashed against the crossbar, and that was as good as it got for the two-time champions as Zamalek held on for the win.
The victory sends the Egyptian giants to the second round of the competition alongside South African side Mamelodi Sundowns, while Enyimba will have to return another year.