Previous studies on emergency management of large-scale urban networks have commonly concentrated on system development to off-load intensive computations to remote cloud servers or improving communication quality during a disaster and ignored the effect of energy consumption of vehicles, which can play a vital role in large-scale evacuation owing to the disruptions in energy supply. Hence, in this paper we propose a cloud-enabled navigation system to direct vehicles to safe areas in the aftermath of a disaster in an energy and time efficient fashion. A G-network model is employed to mimic the behaviors and interactions between individual vehicles and the navigation system, and analyze the effect of re-routing decisions toward the vehicles. A gradient descent optimization algorithm is used to gradually reduce the evacuation time and fuel consumption of vehicles by optimizing the probabilistic choices of linked road segments at each intersection. The re-routing decisions arrive at the intersections periodically and will expire after a short period. When a vehicle reaches an intersection, if the latest re-routing decision has not expired, the vehicle will follow this advice, otherwise, the vehicle will stick to the shortest path to its destination. The experimental results indicate that the proposed algorithm can reduce the evacuation time and the overall fuel utilization especially when the number of evacuated vehicles is large.