With a spike in popularity and sales, the electric vehicles (EVs) have revolutionized the transportation industry. As EV technology advances, the EVs are becoming more accessible and affordable. Therefore, a rapid proliferation of light-duty EVs have been noticed in the residential sector. Even though the increased charging demand of EVs is manageable in large-scale, the low-voltage (LV) residential networks might not be capable of managing localized capacity issues of large scale EV integration. Dynamic electricity tariff coupled with demand response and smart charging management can provide grid assistance to some extent. However, uncoordinated charging, if clustered in a residential distribution feeder, can risk grid assets because of overloading and can even jeopardize the reliability of the network by violating voltage constraints. This paper proposes a coordinated residential EV management system for power grid support. Charging and discharging of residential EV batteries are coordinated and optimized to address grid overloading during peak demand periods and voltage constraint violations. The EV management for grid support is formulated as a mixed-integer programming based optimization problem to minimize the inconveniences of EV owner while providing grid assistance. The proposed methodology is evaluated via a case study based on a residential feeder in Sydney, Australia with actual load demand data. The simulation results indicate the efficacy of the proposed EV management method for mitigating grid overloading and maintaining desired bus voltages.