  We investigate the $\psi(3770)$ non-$D\bar{D}$ decays into $VP$, where $V$
and $P$ denote vector and pseudoscalar mesons, respectively, via
OZI-rule-evading intermediate meson rescatterings in an effective Lagrangian
theory. By identifying the leading meson loop transitions and constraining the
model parameters with the available experimental data for $\psi(3770)\to
J/\psi\eta$, $\phi\eta$ and $\rho\pi$, we succeed in making a quantitative
prediction for all $\psi(3770)\to VP$ with $BR_{VP}$ from 0.41% to 0.64%. It
indicates that the OZI-rule-evading long-range interactions are still playing a
role in $\psi(3770)$ strong decays, and could be a key towards a full
understanding of the mysterious $\psi(3770)$ non-$D\bar{D}$ decay mechanism.
