Victory moved the Syli Nationale up to 11 points, two behind Mali who had already booked their spot at next year's showpiece in Cameroon ahead of the tie after the Confederation of African Football (CAF) disqualified Chad from the remainder of the qualifiers for government interference.
As a result, both Mali and Namibia were awarded 3-0 wins but the Brave Warriors' chances of reaching back-to-back Afcon tournaments have come to an end, with Sunday's match against Guinea in Windhoek now a dead-rubber following the outcome in Conakry.
The defining moment of a largely uneventful encounter came in the 75th minute. Seydouba Soumah pounced on the loose ball on the edge of the area before finding the back of the net with a powerful effort that fizzed past the Les Aigles shot-stopper.
Guinea will move top of Group A with a win in Namibia on Sunday, with Mali's qualification campaign having run its course.
Meanwhile Burkina Faso qualified for the Africa Cup of Nations in Cameroon next January, while Ethiopia trounced Madagascar 4-0.
The Burkinabe secured a place for the sixth time in their last seven attempts by forcing a 0-0 Group B draw away to Uganda near Kampala.
Uganda must avoid defeat in Malawi Monday to join Burkina Faso at the 24-team tournament, which has been delayed one year by the coronavirus pandemic.
Malawi kept hopes of a first Cup of Nations appearance since 2010 alive by edging South Sudan 1-0 through a Richard Mbulu goal in Sudan as the national stadium in Juba is being renovated.
Burkina Faso and Guinea join defending champions Algeria, Mali, Senegal, Tunisia and automatic qualifiers as hosts Cameroon in securing places, leaving 17 places up for grabs.
Africa Cup of Nations qualifiers results (5th round).
Wednesday 24 March
Chad 0-3 Namibia
Guinea 1-0 Mali
Scorer: Soumah 76
South Sudan 0-1 Malawi
Scorer: Mbulu 47
Uganda 0-0 Burkina Faso
Sao Tome and Principe 0-2 Sudan
Scorers: Abdel-Rahman 27, Bakhit 53
Rwanda 1-0 Mozambique
Scorer: Byiringiro 69
Ethiopia 4-0 Madagascar
Scorers: Gebremichael 19, Kebede 34, Nassir 41, Godo 86.