Jermaine Seoposenwe struck twice for Banyana Banyana to go with goals from teammates Amanda Dlamini, Refiloe Jane and Sanah Mollo at Dobsonville Stadium.
Vera Pauw's charges will face Kenya in the third round of qualifying in July after the East Africans edged Botswana on the away goals rule following a 2-2 stalemate across two legs.
Banyana, who won 3-2 in Libreville last weekend, dominated the rematch from the onset, as Seoposenwe opened the scoring in the ninth minute with a composed chip for her eighth international goal.
Dlamini doubled the advantage with a deflected effort into the corner of the net from the edge of the area in the 24th minute.
Jane added a third goal four minutes later when she skipped past her marker in the box before calmly placing her shot past the goalkeeper.
Seoposenwe completed her brace in the 58th minute with a tap-in on the rebound after the ball struck the woodwork.
Mollo then sealed the rout with a header off a right-wing cross in the 77th minute.