Shakes Mashaba had made four changes to the side that drew 0-0 with Gambia in a 2017 Africa Cup of Nations qualifier at the weekend, with Patrick Phungwayo, Clayton Daniels, Bongani Zungu and Jabulani Shongwe coming into the side.
It seemed to pay off as the hosts dominated the early exchanges - without creating too many opportunities - but it was the visitors who would take the lead.
It came on 19 minutes courtesy of a stunning 25-yard strike from Mfutila, which leaft Itumeleng Khune with no chance as it bounced in off the underside of the bar. This after Bongani Zungu lost possession in midfield.
Thamsanqa Gabuza then missed two gilt-edged chances - first from a header and then mis-controlling with just the goalkeeper to beat after some fantastic skill by Thulani Serero.
However, the Orlando Pirates man got his goal in first half injury-time, following up well to bury the ball after May Mahlangu's blistering shot was parried into his path. It was Bafana's first goal in more than 300 minutes.
Bafana again started strongly after the restart, with Gabuza hitting the side-netting while Ayanda Patosi forced a sharp save out of visiting goalie Mavanga, but the second goal did eventually come on 68 minutes.
Anele Ngongca's pass found Serero, whose deft lay-off saw Patosi in on goal. The Lokeren midfielder calmly chipped the goalkeeper, but the ball came back off the underside of the bar, only for substitute Malanda to bundle it into his own net.
Bafana were well worth the lead, and came close again when Thulani Hlatshwayo's header from a corner-kick was saved.
However, the closest we came to another goal was in the 86th minute when Amandio da Costa broke through and chipped the onrushing Khune, only for Thabo Matlaba to clear off his line.
South Africa: Khune, Ngcongca (Nyauza 83), Daniels (Hlatshwayo 72), Coetzee, Phungwayo (Matlaba 59), Zungu, Shongwe (Jali 83), Patosi (Masango 89), Serero, Mahlangu, Gabuza (Ntuli)
Angola: Mavanga, Mafuta, Bondo David, Troco, Estevao (Manuel Alfonso 61), Satonho, Diniz, Justo, Zalata (Malanda 61), Mfutila, Ginga Luis (Amandio da Costa)