"I thought our game plan today was very good. We made sure that we took the game to this team from the beginning," said Bafana Bafana coach Gordon Igesund.
"I went with a very offensive team today and I thought it would work for us, and it did work for us."
Bernard Parker scored Bafana Bafana's first goal in the 27th minute after he was fed by Siphiwe Tshabalala, who had a blinder of a game.
Tshabalala then doubled their tally shortly before the half-time break , and Katlego Mashego netted a header in second-half injury time to seal the win.
"I was a little disappointed because we sat back," Igesund said.
"The second half was a bit of a scary performance from the players. They were scared to lose the game.
"We were 2-0 up. We should have played possession, kept the ball, kept going, and we could have scored four or five more."
Earlier, Ethiopia beat Botswana 2-1 in Lobatse to remain top of Group A in the second round of African qualifying for the 2014 showpiece.
South Africa remained two points behind in second position, while CAR and Botswana were third and fourth respectively, with no chance of qualifying for the Brazil spectacle.
South Africa face Ethiopia in Addis Ababa next week in a crucial clash for top spot in the table.
Central African Republic 0
South Africa (2) 3 (Parker 25’, Tshabalala 42’, Mashego 91’)
Teams:
Itumeleng Khune, Anele Ngcongca, Ricardo Nunes, Thabo Nthethe, Eric Mathoho, Dean Furman, Reneilwe Letsholonyane, Siphiwe Tshabalala, May Mahlangu, Bernard Parker, Tokelo Rantie.