Manucho had equalised for Angola with a 25-yard screamer in an exciting game in Kumasi.
But a defensive error from Kali allowed Zaki to score when he met a cross with his chest on 38 minutes.
The Egyptians progress to meet favourites Ivory Coast in Thursday's semi-final in what is a repeat of the 2006 final.
Not a lot has changed since you went over Rui. We've just lost our manager, assistant and coach, got a new boss and assistant and just won one game since!