After a drab game with few chances for either side, Nekundi found space on the left of the penalty area and fired a shot into the roof of the net in the second minute of injury time.
The win means Namibia play Zambia on Monday with ‘top spot of Group B still at stake’, while Uganda are out of the tournament.
Zambia secured their place in the quarter-finals with a 2-0 victory over Ivory Coast earlier on Thursday.
Chipolopolo top the group on six points, just above Namibia on goal difference meaning that the two southern African teams have now booked their passage to the quarterfinals of the tournament.
On the pitch, Uganda created numerous chances but Allan Kyambadde, Derrick Nsimbabi and Milton Karisa all failed to break the deadlock as the Namibia defence marshaled by the lanky Rian Hanamub stood firm.
Namibia found their rhythm in the second half as they troubled Cranes with square passes and quick counter attacks along the flanks.
Deploying a packed midfield, the debutants, playing in their first ever African Nations Championship tournament, grew in confidence as they sought to register their second straight win in the opening rounds.
Namibia’s best opportunity then came in the 63rd minute when Hendrik Somaeb rushed onto a long upfield clearance and chipped the ball over Uganda’s outrushing keeper only to see the ball skim over the crossbar.
Four minutes later Cranes got a chance but Allan Kyambadde blasted a shot well over when unmarked and Derrick Nsimbabi went close for the Cranes with a header.
Uganda had two more great chances within two minutes, as Nsibambi’s shot from an acute angle went narrowly wide, while Loydt Kazapua once again pulled off a diving save to tip away a scorching shot by Nico Wadada.
The East Africans were reduced to 10 men when defender Timothy Awany was harshly awarded a second caution and sent for an early shower.
This handed Namibians advantage and they could have scored in the 85th minute but Paudeleni Nekundi missed a great chance as his shot went straight Uganda’s keeper, Isma Watenga.
An otherwise quiet Nekundi showed great composure late on to check his shot after receiving a pass from Itamunua Keimuine and fired the ball high into the net to give Watenga no chance.
Uganda: Watenga, Wadada, Awany, Muwanga, Muleme, Mutyaba (Batte 85’), Lwanga, Sadam (Mucurezi 56’), Karisa, Nsibambi, Kyambadde (Senkatuka 75’)
Namibia: Kazapua, Ngaruka, Hambira, Karongee, Hanamub, Ilmbondi, Fredericks, Ketjijere, Shitembi (Katjiteo 87’), Theophilus (Nekundi 58’), Somaeb (Keimuine 46’