Tito Okello scored South Sudan’s only goal during a group B duel at Nyayo National Stadium, Nairobi on Monday.
The former Vipers SC player scored in the 35th minute, a successful kick from the penalty spot after Makueth Wol was brought down by Abdul Karim Watambala in the area.
Two minutes before the goal came, Uganda Cranes has lost midfielder Khalid Aucho after red card offence.
Gallant efforts by Faruku Miya, Emmanuel Arnold Okwi and the entire team in typical fighting spirit to find the equalizer and possible winning goal were frustrated by the mean South Sudan defence.
South Sudan were also reduced to 10 men with 10 minutes to play through Abdallah Musa for a second booking.
Uganda Cranes remains on seven points from four matches while South Sudan earned their first victory of the campaign and has three points.
Group B is led by Burkina Faso who picked an away point off Malawi in Blantyre during the goalless draw.
Burkina Faso has eight points ahead of the next qualification rounds in March 2021.