The comprehensive study of the ab initio pair potentials and prediction of properties for acetonitrile and methanol [J. Chem. Phys. 116, 7627 (2002), preceding paper] is extended to examine the vapor-liquid equilibria of their mixture. An ab initio pair interaction potential is developed for the acetonitrile-methanol interaction consistent with the pure component pair potentials using symmetry-adapted perturbation theory with a double zeta quality basis set including bond functions. Interaction energies were calculated for a large number of configurations to obtain a good representation of the potential energy surface, and employed to develop a site-site pair interaction potential. The ab initio pair potentials for the like and unlike interactions were then used in Gibbs ensemble Monte Carlo simulations to predict the phase behavior of the acetonitrile-methanol mixture. Simulations were performed to determine the phase boundary of the mixture, and although the predicted equilibrium concentrations are not in perfect agreement with experimental measurements, the predicted and measured phase boundaries are similar, including the occurrence of an azeotrope in close agreement with experiment. This prediction of mixture phase behavior is the first reported using ab initio potentials for both like and unlike interactions without the use of any combining rule.