A brace from Junior Nare late on in the match was no enough to overturn the deficit as Prince Mumba and a double from Lameck Banda handed Zambia the three points at the St Francois Xavier Satdium in Port Louis, Mauritius.
The young Chipolopolo were clinical in the first half as they took their chances and went into the half-time break at 3-0 up, with Mumba netting the opener in the 20th minute.
Banda then doubled the scoreline five minutes later, before adding a third three minutes before the half-time mark.
Molefi Ntseki put out an improved performance in the second stanza and midfielder James McFarlane came close to scoring in the 79th minute but was unlucky to strike the post.
However, four minutes later Nare pulled one back and managed a second goal in the 88th minute, but it was too little too late for Amajimbos.
South Africa now sit second in Group B with three points, as Zambia top the standings with six points, from two games thus far.
Group B rivals Mozambique and Madagascar face-off in the day's second clash, with both teams still in search of theor first points on the board.