Three second half penalties from fly-half from Tichafara Makawanya helped the Sables withstand a ferocious fight-back from their hosts who trailed 17-10 at half time.
Makawanya put his side ahead in the third penalty but Kenya responded in style with a converted try from eighthman Lawrence Buyachi to lead 10-3.
Zimbabwe responded quickly with two well worked tries from winger Gardner Nechironga to take the lead at half time.
Makawanya extended Zimbabwe’s lead to 20 -10 soon after the interval. Kenya’s forwards then came to fore as they took the game to their Sables’ counterparts.
Their work eventually as they laid siege on the Zimbabwe line. After a period of sustained pressure, Kenya spun the ball to Victor Sudi to score in the corner to narrow the score to 20-15.
Peter Abuoga added two more penalties later in the half but Makawanya’s prowess with the boot helped the visitors sail through.