Coach Maud Khumalo charges came into this game 2-0 down from the first leg played in Bujumbura a week ago to win the tie 5-2 on aggregate.
The team was inspired by the return of skipper Linda Motlhalo who scored a brace and a goal each by Khanya Xesi, Lelona Daweti and Gabriela Salgado.
Motlhalo missed the first leg due to school commitments as well as Daweti.
Basetsana will go up against the winners between Nigeria and Morocco in the final round in January.
The Under-20 women’s World Cup is set to be played in France next year.