Mohamed Salah provided the decisive moment, lashing in a free-kick through a gap in Ghana’s defensive wall.
A mistake by Ghana keeper Brimah Razak presented Marwan Mohsen with a chance to double the lead but he shot over.
Daniel Amartey missed Ghana’s best chance, heading wide from Christian Atsu’s free-kick to the back post.
The result means Egypt will face Morocco and Ghana will take on DR Congo in last-eight matches on Sunday.
