This paper first presents a time-series impact analysis of charging electric vehicles (EVs) to loading levels of power network equipment considering stochasticity in charging habits of EV owners. A novel incentive-based mitigation strategy is then designed to shift the EV charging from the peak hours when the equipment is overloaded to the off-peak hours and maintain equipment service lifetime. The incentive level and corresponding contributions from customers to alter their EV charging habits are determined by a search algorithm and a constrained optimization problem. The strategy is illustrated on a modified version of the IEEE 8500 feeder with a high EV penetration to mitigate overloads on the substation transformer.