The only goal of the game was a headed effort on 74 minutes as Kizito took advantage of slack Kenyan defending to capitalise and hands the Cranes the three points.
It means that they climb joint top of Group A with three points, same as Ethiopia who earlier beat South Sudan 1-0.
The first half was shaded by the Cranes, who had the lions share of goal-bound opportunities, pressing the Kenyans deeper and deeper into their area.
The best chances for the Cranes went to Emmanuel Okwi who shot wide on three different occasions when well placed, while the Kenyans had no clear opportunity on goal, with a Rama Salim run in on goal one of the best signs in attack.
Kenya improved towards the end of the half but again they could not convert, especially when Humphrey Mieno went through on goal.
In the second half the Stars looked better as they brought on Paul Were who created a chance for Rama Salim but he could not convert.
Mieno also had another good chance but he shot over the bar as the Stars struggled to get any added effort on goal and they were made to pay by Kizito who headed home off Dennis Guma's free-kick.
The introduction of Enoch Agwanda with ten minutes to go revitalized the Stars as his long throws caused the Cranes all sorts of problems, with one just getting cleared at the death and another hitting the post in the last minute.
However, they could not muster really clear effort on goal and will have to look to their clash with South Sudan on Tuesday 27 November 2012 to try register their first points.