The club based in a rugby union hotbed 60 kilometres (37 miles) from Cape Town overcame the sending off of Ismael Toure to force a 1-1 draw with V Club in Kinshasa and win 3-1 on aggregate.
A man short, Stellenbosch silenced a crowd that filled most of the 80,000-seat national stadium by taking the lead on 71 minutes through new signing Lehlohonolo Mojela.
That goal left 2018 Confederation Cup runners-up V Club needing to score at least four times to win the second round qualifier.
But all the Congolese could manage was a second-leg equaliser when Comoran Affane Djambae converted a penalty kick deep in added time.
While V Club are less of a force than in previous decades, it was a significant achievement for Stellenbosch to draw in front of some of the most partisan supporters in the continent.
Orapa United upset Zimbabwean opponents Dynamos to become the first Botswana club to reach the group stage in the African equivalent of the UEFA Europa League.
A 72nd-minute goal from Namibian Ivan Kamberipa earned Orapa a 1-0 win. With the teams deadlocked at 1-1 on aggregate, the tie was settled by a penalty shootout that United won 3-1.
Nigerian challengers Enyimba also needed penalties to reach the group stage, where each qualifier is guaranteed $400,000 (€360,000) prize money plus a $50,000 participation fee.
After two 0-0 draws with Etoile Filante of Burkina Faso, two-time CAF Champions League winners Enyimba prevailed 3-2 in a shootout in southeastern city Uyo.
Tanzanian outfit Simba came from behind in Dar es Salaam to beat Libyan visitors Al Ahly Tripoli 3-1 and win by the same score on aggregate.
Angolan Mabululu put Ahly ahead, Denis Kibu levelled and Cameroonian Leonel Ateba scored in added time to give the hosts a 2-1 half-time advantage.
Fadlu Davids, the South African coach of Simba, endured a tense second half before an 85th-minute Edwin Balua goal ensured qualification.
© Agence France-Presse
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