A difficult opening half made way for a totally dominant second as Vilakazi netted twice in six minutes, before debutant Bongani Ndulula applied the finishing touches with a third to send South Africa into pole position with three points and to top group A.
Met by a hostile reception from a capacity crowd at Al-Merrikh Stadium, South Africa handed coach Shakes Mashaba his first victory in his first game since being hired for a third term in July.
In a week of soaring temperatures and staggering humidity, Bafana put up a professional display.
Vilakazi celebrated his first international goals for his country, despite starting on the bench.
Ndulula was also rewarded with a full 90 minutes and opened his account.
Fellow debutant Keagan Dolly lasted the first-half and was substituted at the break.
Despite the early pressure from the hosts, Bafana had the first real chance.
Sudan goalkeeper Elmoiz Mahgoub spilled a cross from the right, allowing Tokelo Rantie to pounce, but the striker pushed his effort narrowly wide nine minutes into the match.
Bafana captain Senzo Meyiwa was forced into action shortly after, twice denying Ramdan Agab.
The second effort produced a superb diving stop from the Orlando Pirates shot-stopper, getting his fingertips to a long-range effort that was destined for the top corner.
South Africa struggled to get a hold of the game and often found themselves camped in their own half for extended periods.
Meyiwa was kept the busier of the two goalkeepers and made a handful of saves as Sudan began to stamp their authority in testing conditions.
Rantie looked lively and called Mahgoub into action after the half-hour mark when he spun on the ball and thundered a left-footed effort goal-bound.
Mahgoub palmed away the shot to deny the burly attacker, who looked dangerous every time he had the ball at his feet.
With scores goalless at the break, Bafana headed out looking to put the home side under pressure from the onset.
The visitors changed their line-up as Mashaba brought on Vilakazi, who made an immediate impact and had Sudan rattled with virtually his first touch.
The Wits playmaker won a corner for South Africa, from which he stabbed home following a scramble in the area.
Thulani Hlatshwayo looked to seize theopportunity but his dangerous effort was cleared off the line. Vilakazi was on hand and neatly beat out a host of defenders camped out in the goalmouth, handing South Africa the advantage 10 minutes after the restart.
But more was to come from the “super-sub” who buried his second of the night and sent South Africa two clear six minutes later.
Some solid build-up play saw Bafana control possession on the edge of the area, before Vilakazi eventually took responsibility and shot past the hapless Sudan goalkeeper.
The goal knocked the wind out of Sudan’s sails as South Africa continued to surge forward.
Vilakazi was brilliant on the ball with every touch and put in a Man-of-the-match performance.
The victory will go a long way in building confidence ahead of Bafana’s return to the country for their second qualifier against Nigeria, in Cape Town on Wednesday.
** Sapa reporter is in Khartoum as a guest of SA Football Association.