The two sides had never met each other in a competitive match before Friday's encounter at Al Merreikh Stadium and, although Sudan played the better football for long stretches, the visitors emerged as victors in their Group A opener.
Mashaba, who replaced former boss Gordon Igesund, selected a relatively inexperienced squad for South Africa's first game since May and had to make do without first-choice goalkeeper Itumeleng Khune due to injury.
However, it did not matter a a second-half double from Sibusiso Vilakazi and one from Bongani Ndulula secured a comfortable triumph.
Both sides looked threatening during the opening stages as South Africa's Mandla Masango missed the target from close range, before goalkeeper Senzo Meyiwa was forced to deny Sudan at the other end.
South Africa went close again in the 32nd minute as Tokelo Rantie saw his powerful drive parried away by Moez Mahgoub, and they finally capitalised on Sudan's wastefulness by taking the lead just after the break.
Vilakazi pounced on a loose ball in the area before steering home in the 56th minute and his second swiftly followed.
The midfielder raced on to a defence-splitting pass and coolly slotted past the helpless Moez to give South Africa a commanding lead with 61 minutes gone.
The result was put beyond all doubt in the 79th minute as Ndulula tapped in Oupa Manyisa's cross to open up a three-goal lead.
Sudan almost grabbed a late consolation but Mohammed Mousa's header struck a post.
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