There were two changes for Banyana from their first-leg win on Friday in the form of captain Janine Van Wyk and Gabriela Salgado.
It was a quiet start to the clash, but the South Africans began to take charge towards the closing quarter and closed in through Kholosa Giyana's rasping shot outside the area.
Algeria began to take control moments thereafter and did have the ball in the net, but it was disallowed after a foul was committed on goalkeeper Andile Dlamini.
The North Africans did grab the lead on the brink of halftime through a finish from Sylia Koui as the South Africans failed to keep their lines from a defensive point of view.
In the second half, the North Africans started on the front foot and left Banyana Banyana to chase the contest in light of overturning the outcome in the grand scheme of things.
Banyana did grab the equaliser in the middle of the second half when a hand ball in the area by Algeria led to a penalty-kick, which Linda Motlhalo converted.
Desiree Ellis's side maintained the balance of play shortly before fulltime, and furthermore freshened up matters with the introduction of Sibulele Holweni for Salgado.
There was no late drama from the hosts in the close stages, as the South African women managed matters and clinched the overall tie whilst progressing to the AWCON tournament in Morocco in July this year.