Egypt broke the deadlock in the 59th minute when a handball resulted in a penalty kick which Ramadan Sobhi converted after sending Darren Johnson the wrong way.
Singh threatened to level matters in the final eight minutes, though Singh saw his free-kick cracked the crossbar.
Abdel-Rahman Magdi went and forced himself down the right to rifle home a close-range shot two minutes later after the visitors failed to clear their lines.
Magdi had a double within the matter of five minutes when a howler from Johnson helped the former’s probing attempt to an unguarded net.
South Africa will now have to play Ghana for a third place and hope to qualify for the Olympic Games through that same route just as in 2016.