Then Kyle missed a more gilt-edged chance when his effort went just over after Vonk had misjudged a Williams free kick.
Lee Wilkie won his first cap when he replaced Gary Caldwell at half-time and the Dundee defender went on to produce an impressively assured performance.
Scotland again came close to equalising four minutes into a second period during which Motherwell's James McFadden became the latest to win his first Scotland cap.
Dobie sent Kyle clear, but his flick over the advancing goalkeeper struck the face of the crossbar.
South Africa were again reduced to long-range efforts, while Ross came close to catching Vonk off his line with a long-range chip at the other end.
But Basle forward Koumantarakis settled the match in injury-time with a low drive as the Scots were caught out pressing forward for the equaliser.
South Africa: Vonk, Aaron Mokoena, Radebe, Issa, Carnell, Zuma,
Sibaya, Fortune, Pule, McCarthy, Teboho Mokoena. Subs: Arendse,
Marlin, Nzama, Mngomeni, Mukansi, Mnguni, Nomvete, Buckley,
Pienaar, Molefe, Koumantarakis.
Scotland: Douglas, Stockdale, Caldwell, Dailly, Weir,
Ross, Gemmill, Williams, Dobie, Kyle, Johnston. Subs:
Gallacher, Neil Alexander, Graham Alexander, Stewart,
O'Connor, Wilkie, McFadden, Cummings, Thompson, Severin.
Referee: Chan Siu Kee (Hong Kong).