Large-scale development of electric vehicles (EVs) exposes power grids and transportation networks with limited capacity to increased fault risks. In this paper, a method to prevent fault risks in advance by using the flexibility of EV travel to coordinate the operation of distribution and transportation networks is proposed. Since EV travel decisions are influenced by the charging and travel time costs, adjusting charging price and travel time price can help guide behavior and enable coordinated operation of power and transportation networks. First, risk-based distribution locational marginal prices (RDLMPs) are established to restrain the distribution network risks. Second, traffic risks are formulated using origin-destination (OD) risk marginal prices (ODRMPs) considering the degree of traffic congestion fault risks. Under the guidance of the RDLMPs and ODRMPs, EV fleets optimize their travel plans to minimize overall costs, including charging and time costs. Finally, case studies verify that the proposed method can reduce the operational risks of both distribution and transportation networks.