  We generalize a complex heavy-quark potential model from an isotropic QCD
plasma to an anisotropic one by replacing the Debye mass $m_D$ with an
anisotropic screening mass depending on the quark pair alignment with respect
to the direction of anisotropy. Such an angle-dependent mass is determined by
matching the perturbative contributions in the potential model to the exact
result obtained in the Hard-Thermal-Loop resummed perturbation theory. An
advantage of the resulting potential model is that its angular dependence can
be effectively described by using a set of angle-averaged screening masses as
proposed in our previous work. Consequently, one could solve a one-dimensional
Schr\"odinger equation with a potential model built by changing the anisotropic
screening masses into the corresponding angle-averaged ones, and reproduce the
full three-dimensional results for the binding energies and decay widths of
low-lying quarkonium bound states to very high accuracy. Finally, turning to
dynamics, we demonstrate that the one-dimensional effective potential can
accurately describe the time evolution of the vacuum overlaps obtained using
the full three-dimensional anisotropic potential. This includes the splitting
of different p-wave polarizations.
