Unmarked Sunday Faleye wasted a great chance to snatch victory for the Nigerians in the final minute by heading a cross wide when a goal seem inevitable.
Ivory Coast edged Zambia 1-0 through a goal from centre-back Kouadio-Yves Dabila in the other Group B match of an eight-nation qualifying competition.
The final group matches were played simultaneously in the Egyptian capital with all four countries in contention for semi-finals places before the kick-offs.
Ivory Coast (six points) topped the final standings followed by South Africa (five) and they advanced to the semi-finals next Tuesday while Nigeria (four) and Zambia (one) head home.
Impressive Group A winners Egypt will face South Africa at the penultimate stage followed by the Ivory Coast against Group A runners-up Ghana.
The semi-finals winners are guaranteed places at the Tokyo Olympics while the losers get a second chance in the third place play-off to fill the third and last African slot.
Egypt have competed at Olympic football tournaments 11 times — a record for an African nation, but have never collected medals.
Ghana will be seeking a seventh appearance, South Africa a third and the Ivory Coast a second at a tournament where Nigeria (1996) and Cameroon (2000) have won gold.
Olympic qualifying is restricted to under-23 footballers, but three ‘over-age’ stars are permitted at the finals.