Nigeria were back in the country where they won the African Nations Cup this year and Dutch-based striker Nwafor, playing only his second international, scored with an audacious back heel to give the visitors the lead in the 49th minute.
Nwofor reacted quickest with his back to goal and improvised with some power to beat South Africa goalkeeper Itumeleng Khune.
He got his second goal in the 68th minute at the end of an swift passing movement involving Victor Moses and Ahmed Musa, whose quick movement cut through the home defence to set up an easy tap-in for the VVV Venlo forward.
Moses and Russian-based Musa were brought on at the start of the second half to inject more pace into the Nigeria attack.
"I knew the South Africans were planning on them starting so I kept them for an impact in the second half," coach Stephen Keshi told reporters.
South Africa created several chances but were let down by poor shooting, particularly after making space for themselves on the edge of the Nigeria box.
It was a sixth loss in eight outings for Bafana Bafana against the African champions, whose next assignment is a key World Cup qualifier against Malawi next month.
Nigeria need only draw on Sept. 7 at home in Calabar to win their group and qualify for the final round of African qualifiers.
"We need to get more rhythm and work more on our possession and tactical play. If we get that right and the attitude is there, we can progress," Keshi told a news conference.