But Harambee Stars will have themselves to blame as they created numerous scoring chances but failed to find the back of the net with captain Michael Olunga, Kenneth Muguna and Masud Juma the key culprits.
Muguna could have drawn level before the half hour mark after a brilliant team build up, but his effort was superbly blocked by Bright Stars goalkeeper Joseph Anyuma for a fruitless corner.
Olunga then had a clear cut chance to equalise midway through the second half, but the Al Duhail man fluffed his lines on a one-on-one situation with Anyuma as the visitors resorted to defensive tactics, waiting to hit Kenya on counter attack.
Olunga's miss happened moments after Bradford City midfielder Clark Oduor finally made his eagerly awaited Harambee Stars return by replacing Masud Juma on the hour mark as Duke Abuya came on for Muguna.
With that victory, South Sudan have shown that they are slowly but surely becoming a force to reckon with in the East Africa region.
Despite numerous raids, Stefano Cusin's boys held their nerves to secure the win and bounce back in style from last Friday's 4-0 away defeat to Mali in AFCON qualifiers.