Connectivity in a smart vehicular network is quite sensitive and highly affected by its dynamic network topology. Issues related to the intermittent nature of connectivity may arise due to the high mobility of nodes and network heterogeneity. In sparse areas, a vehicular network is basically a disruption-tolerant network suffering from frequent disconnections, long delays, and messages loss.Facing these issues, and specifically for time-sensitive applications, Unmanned Aerial Vehicle (UAV) can provide valuable assistance to Vehicular Ad Hoc Network (VANET) by assuming a relay node role between disconnected segments in the road. In such scenarios, effective communication is either between vehicles (V2V) or between vehicles and UAVs (V2U), which would form subsequently a UAV-assisted vehicular network. In the present paper, we propose a new framework for using small UAVs as mobile infrastructure nodes in order to enhance the connectivity between vehicles. The first part of this framework accurately predicts the disconnected segments such that drones can be deployed to reestablish lost links. We have implemented a theoretical game for this prediction process. Furthermore, since the battery reserves of the UAVs are limited, we have proposed a mitigation technique based on game theory to reduce the power draining effects that a broadcast storm would have on the energy consumption of the network. For the validation of the proposed UVE (UAV-aided VANET framework, with energy-conscious constraints), we conducted thorough simulation scenarios with Network Simulator 3. The obtained performances are promising in the sense that our approach achieves high packet delivery ratio, low end-to-end delay, and low overhead communication costs.Trans Emerging Tel Tech. 2019;30:e3520.wileyonlinelibrary.com/journal/ett