Bafana coach Molefi Ntseki made wholesale changes to the side that lost against Ghana on Thursday, with Thapelo Morena and Erick Mathoho drafted to the back-line, while Kamohelo Mokotjo, Thulani Serero and Lebogang Mothiba and Phiri got called to the side.
Morena should have put Bafana ahead in the second minute after being teed up by Serero but he side-footed his shot wide despite having a lot of space, before Mothiba squandered a big chance in the 14th minute from six-yards out.
After a spell of missed opportunities, impressive inter-play between Tau and Serero set up Mokotjo, who almost broke the deadlock with a thumping strike that was smothered by goalkeeper Ali Aboeshren.
Phiri eventually found the breakthrough for the hosts on the stroke of halftime with a cracking left-footed strike that sailed into the top corner after Sudan failed to clear their lines from another Bafana attack.
The North African side were showing their hand early in the second stanza, no longer sitting deep in their own half and growing in the game with threatening counter-attacks but Bafana were alert at the back.
South Africa were finding joy through the right channel operated by Morena, who served up a few decent crosses into the box but Aboeshren made two crucial interceptions to deny Mothiba the simple finish.
Ntseki was searching for an insurance goal with 20 minutes remaining, as he brought on Lebogang Manyama and Kermit Erasmus for Phiri and Mothiba, while Bradley Grobler replaced Serero soon after.
Grobler found the back of the net for Bafana in the last eight minutes with a tap-in after Aboeshren parried Erasmus' header into his path, but the goal was ruled out for offside as the encounter finished 1-0, with Bafana claiming their first win in Group C.
Bafana: Ronwen Williams, Thapelo Morena , Sfiso Hlanti , Erick Mathoho, Thulani Hlatshwayo (C), Kamohelo Mokotjo , Dean Furman , Lebohang Phiri , Percy Tau , Thulani Serero, Lebo Mothiba
Subs: Keet (GK), Goss (GK), Lebusa , Mkhwanazi , Lorch , Manyama, Mvala , Modiba , Maela , Grobler, Mokeke, Erasmus.
Sudan: Aboeshren, Atahir Mohamed, Suliman, Ismaeil, Mahmoud Ahmed, Mahamoud, Shareif, Abdelrahman, Hamid.