[en] We calculate strong interaction O(α_s) corrections to the effective one-loop induced neutral flavour changing vertex anti sdZ for an arbitrary top quark mass in 't Hooft-Feynman gauge for the W-field. This two-loop calculation is necessary for a meaningful use of a running top quark mass in rare K- and B-decays and consequently increases the precision of theoretical predictions. We find that the uncertainty in the strength of the effective vertex anti sdZ, due to the dependence of m_t on the choice of the renormalization scale μ, is reduced from O(10%) to O(1%) by including the O(α_s) corrections. For the choice μ=m_t the corrections are less than 5% for 100≤m_t≤200 GeV but they are substantially larger for μ=M_W. As a by-product we confirm the O(α_sG_Fm_t²) correction to the Z→b anti b partial decay width calculated recently in the large top quark mass limit. (orig.)