Asamoah Gyanâ€™s first half goal put the Black Stars into the semi-finals where they will face the winner of Mondayâ€™s match in Lubango between Zambia and Nigeria.
As a severely depleted Ghana side marched on in search of their first continental crown in 28 years Angola rued not putting away a number of clear cut chances, not least Manuchoâ€™s shot over the woodwork approaching the interval.
Angola made two changes from the side that qualified for the last eight with a goalless draw against Algeria - defender Stelvio returning from suspension and three-goal hero Flavio back from injury to join Manucho up front.
Ghana, missing a raft of star players including Michael Essien, made one alteration from their last run out, Mathew Amoah making way for Qatar-based midfielder Opoku Agyemang.
A minuteâ€™s silence for the victims of the Haiti earthquake preceded this first ever competitive meeting between the two African states.
Ghana into Nations Cup semi-finals