  The non-diagonal correlators of vector and scalar currents are considered at
three-loop order in QCD. The full mass dependence is computed in the case where
one of the quarks is massless and the other one carries mass $M$. We exploit
the decoupling relations between the full theory and the heavy quark effective
theory (HQET) in order to obtain the logarithmic parts of the leading threshold
terms. With the help of conformal mapping and Pad\'e approximation numerical
estimates for the non-logarithmic terms are extracted which in turn lead to a
prediction of the correlator in HQET at order $\alpha_s^2$. As applications of
the vector and scalar correlator we consider the single-top-quark production
via the process $q\bar{q}\to t\bar{b}$ and the decay rate of a charged Higgs
boson into hadrons, respectively. In both cases the computed NLO corrections
are shown to be numerically much less important than the leading ones. On the
contrary, the NLO order QCD corrections to the HQET sum rule for the leptonic
decay rate of a heavy-light meson proves to be comparable to the leading one.
