Australia lost three quick wickets to stand at 143-4 when Hussey, who replaced his brother David in the team after joining the squad on Tuesday, came to the crease in the 27th over.
Hussey (54) shared a 114-run partnership with Clarke for the fifth wicket after opener Brad Haddin scored 65 to leave Kenya's struggling batsmen chasing a daunting total.
Kenya, which has been beaten convincingly in all four matches so far, bowled tenaciously early on, with Nehemiah Odhiambo the pick of the bowlers on 3-57.