Siphiwe Tshabalala was particularly impressive and deservedly gave South Africa the lead with a precise finish.
The hosts continued to press for a second but it took until second-half injury time to tie-up the game when Lerato Chabangu's effort just crept over the line.
South Africa manager Gordon Igesund made five changes to the side that lost 2-0 to Nigeria on Wednesday, and gave opportunities to the younger players in his squad, while African Cup of Nations runners-up Burkina Faso named a near full strength line-up.
The hosts made the brighter start to the game with David Mathebula and Tshabalala looking particularly threatening down the right-hand side.
And it was the latter who got the breakthrough for South Africa in the 22nd minute when some slick passing led to Bongani Zungu feeding Tshabalala in the area and he turned sharply before firing a pin-point effort into the bottom left-hand corner.
The midfielder continued to look dangerous and fired a 25-yard effort just wide of the post.
South Africa's momentum was hindered slightly by the goal, with Burkina Faso enjoying some success at set-pieces.
But it could have been 2-0 before half-time when Reneilwe Letsholonyane smashed a drive against the left post from 30-yards.
The second half continued in a similar fashion with South Africa largely on top of proceedings, and Bernard Parker should have done better in the 57th minute when he headed tamely straight at Mohamed Kabore when unmarked in the box .
Just a minute later Parker did have the ball in the back of the net but he was adjudged offside.
Burkina Faso had a couple of half-chances but seldom threatened the South Africa goal.
And the game was wrapped up in injury-time, when a deflected effort from Chabangu was deemed to have crossed the line.
