We investigate the psi(3770) non-DD decays into VP, where V and P denote vector and pseudoscalar mesons, respectively, via Okubo-Zweig-Iizuka-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)-->J/psieta, phieta, and rhopi, we succeed in making a quantitative prediction for all psi(3770)-->VP with BRVP from 0.41% to 0.64%. It indicates that the Okubo-Zweig-Iizuka-rule-evading long-range interactions play a role in psi(3770) strong decays, and could be a key towards a full understanding of the mysterious psi(3770) non-DD decay mechanism.