The hosts looked relatively comfortable throughout and made the breakthrough in the 36th minute courtesy of a deflected Mohau Mokate effort.
That proved the only goal of the game as Bafana Bafana won what is effectively the competition's fifth-place play-off.
It was in fact Namibia who were afforded the best chance of the opening stanza when Tercious Malepe needlessly hauled down and opponent in the penalty area.
Ronald Ketjijire stepped up to take the resultant spot-kick in the fifth minute but turned his effort wide of Boalefa Pule's upright.
An inability to effectively clear their lines was the story of Namibia's first half and they gave Mothobi Mvala a chance to strike at goal inside 10 minutes but he turned his effort wide.
Judas Moseamedi was proving quite a threat but went down too theatrically in the box to draw a penalty before shooting straight down the throat of Maximilliam Mbaeva.
The deadlock was eventually broken as Namibia again did a sub-par job of getting the ball clear and it dropped to Mokate whose shot from range crashed into a defender and sailed into the net.
Minutes after the break Nduduzo Sibiya had a great chance in the box but failed to pull the trigger as Riaan Hanamub intervened timeously.
As the game approached the hour mark Moseamedi attempted to lob Mbaeva with the stopper off his line but the effort ghosted just wide.
Namibia had enjoyed very little success in front of goal but came close in the 78th minute as Denzil Haoseb looped a header onto the crossbar with Pule beaten.
In the final minutes Namibia pressed hard for an equaliser and with time running out Sandile Mthethwa was forced to clear off the line before Pule saved from point blank range to preserve his side's lead.
South Africa: Pule, Malepe, Booysen, Gordinho, Mvala, Mukumela (Mthethwa 41'), Masalesa, Norodien (Jordan 77'), Mokate (Webber 86'), Sibiya, Moseamedi
Namibia: Mbaeva, Haoseb, Hanamub (Gebhardt 53'), Karongee, Horaeb, Hotto, Katjiteo, Gome (Nenkavu 81'), Ketjijere, Keinmuine (Shalulile 62'), Shitembi