Jody February was the hero for Amaglug-glug as he saved a penalty in regulation time, as well as three spot-kicks in the shootout which culminated with Phakamani Mahlambi's winning kick at Stade Leopold Senghor.
Owen da Gama's side will represent the continent at Rio 2016, along with U-23 AFCON finalists Nigeria and Algeria.
The national women's team, Banyana Banyana, will also compete at the global sporting showpiece in Brazil.
South Africa showed early intent, as Gift Motupa had an effort tipped over by Senegal goalkeeper Pape Ndiaye in the sixth minute.
The hosts, however, wrestled back momentum as Ajax Cape Town keeper February was forced to make a stop 10 minutes later.
Senegal continued to press, with the influential Sidy Sarr and Moumodou Diallo firing shots at February's goal without reward midway through the stanza.
Amaglug-glug's Deolin Mekoa and Motupa had unconvincing attempts at an opener before the exciting Mahlambi tested Ndiaye with a volley just before the interval.
The visitors had a great chance early into the second period, but Motupa pulled his shot wide after being put through one-on-one with Ndiaye by Mahlambi.
The teams proceeded to trade opportunities at either end. Motupa and Orlando Pirates teammate Menzi Masuku were in the thick of things offensively, while February saved a penalty in the 74th minute, with Ibrahima Keita striking the woodwork on the rebound.
Neither side could break the deadlock inside 90 minutes, with South Africa ultimately prevailing on penalties to book a spot at Rio 2016, and gain revenge for a 3-1 loss to the west Africans in the tournament opener.
Senegal XI: Ndiaye, Diedhiou, Cissokho, Sarr, S.Ndiaye, I.Sarr, Diallo, Mbengue, Diaw, Wague, Dieng.
South Africa XI: February, Rikhotso, Mngonyama, Coetzee, Moerane, Mobara, Dolly, P. Ntshangase, Mahlambi, Mekoa, Motupa.