  We revisit the calculation of the strong couplings $D^*D\pi$ and $B^*B\pi$
from the QCD light-cone sum rules using the pion light-cone distribution
amplitudes. The accuracy of the correlation function, calculated from the
operator product expansion near the light-cone, is upgraded by taking into
account the gluon radiative corrections to the twist-3 terms. The double
spectral density of the correlation function, including the twist-2, 3 terms at
${\cal O} (\alpha_s)$ and the twist-4 LO terms, is presented in an analytical
form for the first time. This form allows us to use various versions of the
quark-hadron duality regions in the double dispersion relation underlying the
sum rules. We predict $g_{D^*D\pi}=14.1^{+1.3}_{-1.2}$ and
$g_{B^*B\pi}=30.0^{+2.6}_{-2.4}$ when the decay constants of heavy mesons
entering the light-cone sum rule are taken from lattice QCD results. We compare
our results with the experimental value for the charmed meson coupling and with
the lattice QCD calculations.
