UCU, who have now lost two in a row, were led by Vilma Achieng with 12 points and 14 rebounds.
Maureen Adong led her side to a series game tie at YMCA.
Soigi scored a game high 15 points as the Leopards grabbed victory in the last five minutes.
Flavia Oketcho nailed a game- high 24 points for KCC
KCCA's defence has worried its fans and players alike
Sign up to receive our free newsletter