We calculate strong interaction O(alpha s) corrections to rare K- and B-decays dominated by Z0 penguins and box diagrams with virtual top quark exchanges for an arbitrary top quark mass. We find that the uncertainty in the branching ratios, due to the dependence of mt on the choice of the renormalization scale µ is reduced from O(25%) to O(3%) by including the O(alphas) corrections. For the choice of µ=mt with 100 GeVmt200 GeV the corrections to Kl ->0vv and B ->Xsvv are less than 4% and at most 13% for B->ll. For the choice µ-Mw they can be as large as 20% for both types of decays. We also point out that the published branching ratios for B->ll miss an over-all factor of 2.