Luvuyo Mkatshana netted his third goal of the tournament to ensure South Africa maintain their unbeaten run in Zambia, where they will now fight for the trophy.
It was a tense affair between the two sides who met just three days ago in their group stage fixture, in which Amajita came from behind to win 2-1.
Thabo Senong's boys though proved that it was not a fluke beating the North Africans, as they held tight to ensure no way past their defense.
It was a close battle though, as Mkatshana found the back of the net in the 43rd minute, getting onto Sbusiso Mabiliso's cross into the box before slotting home from close range.
A number of chances went the way of Amajita in the second half but the boys lacked the composure to kill of the game, giving Egypt a few sniffs at goal too.
However, the score remained unchanged as South Africa held their nerve to see out the victory.
They will find out who they will next face when Uganda and Lesotho clash in the second semi-final on Thursday afternoon.