Bafana created a number of chances, with Percy Tau having the best of them, but also survived some nervous moments from the visitors.
The home side looked a little disjointed and did not have the same crispness in their play on show in the 3-1 victory over Guinea-Bissau on Saturday.
Caretaker coach Owen da Gama had named a new-look side with nine changes from that team.
Phakamani Mahlambi, Luther Singh and Diamond Thopola were all been handed their debuts, with Darren Keet taking over from Itumeleng Khune in goal.
Tebogo Langerman continued at left-back, while Thopola occupied the right-back position. Erick Mathoho partnered Rivaldo Coetzee in central defence.
Andile Jali and Tiyani Mabunda pulled the strings from the middle of the park where they were assisted by U-20 internationals Mahlambi and Singh.
Upfront, Lebogang Manyama played alongside Tau.
Langerman and Mathoho were the only two survivors from the Guinea-Bissau victory.
South Africa were much the brighter in the opening 20 minutes with Tau and Mahlambi combining on a number of occasions.
A one-two between the pair set Tau on goal, but he opted for a square-pass on the edge of the six-yard box when he might have taken on the shot himself.
Tau was through on goal again and this time poked the ball past the keeper, but some scrambling home defence managed to clear for the Angolans.
The visitors grew into the game after that and began to see more of the ball, inevitably also creating chances.
The best fell to Herenilson from the edge of the box, but his shot to the corner was expertly beaten away by Keet as the teams went into the break at 0-0.
Da gama made four changes at the break, bringing on Keagan Dolly and Thulani Serero amoung them, and the combination play was better.
But they still battled to force a save from the Angolan keeper Adilson Neblu.
At the other end there was an alarm when Quibeto's shot from range brushed the top of the crossbar, probably as close as either side came to a winner.
South Africa: Keet, Thopola (Mphahlele 46'), Mathoho, Coetzee, Langerman, Jali, Mabunda, Mahlambi (T. Zwane 46'), Manyama (Serero 46'), Singh (Dolly 46'), Tau (Erasmus 74').
Subs: Walters, Khune, Gordinho, Kekana, Mokotjo, Furman, Veldwijk.
Angola: Neblu, Lunguinha, Nary, Bastos, Natael, Manquxi, Leite, Herenilson, Nandinho, Yano, Papel.