Haitham Mustafa hit the target in the 51st minute before Alaa Eldien Yusuf scored the second goal seven minutes later to seal Sudan's victory.
Despite dominating and hitting the target many times, Tanzania were not capable of scoring.
The match was postponed from Friday to Sunday due to heavy rain over Ittihad El-Shorta’s stadium caused Ugandan referee Dennis Batte to deem the pitch unplayable.
The first edition of the friendly tournament will end on Monday when Uganda face Egypt in the final after the third place decider between DR Congo and Kenya.
The Pharaohs booked their place in the final by smashing Kenya 5-1 in the semis, while Uganda reached the final by defeating DR Congo 1-0.