Report by Xinhua
Having lost the first leg 16-13 last month in Kisumu, the visiting Kenyan team needed an outright win if they were to retain the trophy.
Ronald Kanyanya gave Uganda the lead with a try, but Phillip Wokorach missed the conversion. The visiting Kenyan side fought back to score through Billy Odhiambo and Jacob Ojee converted to give them an 8-5 half time lead.
In the second half, Ojee added another try for Kenya and converted a penalty to make it 16-5.
The home side tried to fight back, but failed to break the Kenyan back-line.
"The team played well and I am happy that we came here and won the game having lost at home," Kenya coach Paul Odera told Xinhua.