Basetsana overcame a 2-0 deficit from the first leg to advance to the third round of qualifying, where they will meet either Nigeria or Morocco on the weekends of 12-14 and 26-28 January.
Captain Linda Motlhalo hit a brace to go with strikes from Khanya Xesi, Lalona Daweti and Gabriela Salgado in Soweto on Saturday.
"We are very proud of the ladies and the fact that we converted the five chances," said Khumalo.
"We are happy to have won 5-2 on aggregate and qualify for the third round of the qualifiers.
"We do however need to stay focused and remember that this is not the end but a stepping stone towards the World Cup and next year will be another challenging task."
The U-20 Women's World Cup will take place in France from August 5 to 24 next year.