Next-generation power grids will likely enable concurrent service for residences and plug-in electric vehicles (PEVs). While the residence power demand profile is known and thus can be considered inelastic, the PEVs’ power demand is only known after random PEVs’ arrivals. PEV charging scheduling aims at minimizing the potential impact of the massive integration of PEVs into power grids to save service costs to customers while power control aims at minimizing the cost of power generation subject to operating constraints and meeting demand. The present paper develops a model predictive control (MPC)-based approach to address the joint PEV charging scheduling and power control to minimize both PEV charging cost and energy generation cost in meeting both residence and PEV power demands. Unlike in related works, no assumptions are made about the probability distribution of PEVs’ arrivals, the known PEVs’ future demand, or the unlimited charging capacity of PEVs. The proposed approach is shown to achieve a globally optimal solution. Numerical results for IEEE benchmark power grids serving Tesla Model S PEVs show the merit of this approach.