Power-aware routing and controlled mobility schemes are two commonly used mechanisms for improving communications in a wireless sensor network. While the former actively consider the transmission costs when selecting the next hop on the route, the latter instruct mobile relay nodes either sensors or actuators) to pursue more promising locations so as to optimize end-to-end transmission power. Rarely, if ever, the two methodologies are exploited together for achieving relevant energy savings and prolonging network lifetime. In this paper, we introduce a hybrid routing-mobility model for the optimization of network communications. First, we find a multi-hop path between a source and its destination in an energy-efficient fashion and then we move all hop nodes in an uninterrupted, straight manner to some predefined spots with optimal energy-saving properties, fully preserving the path connectivity as they move. Such synergetic approach allowed us to: (1) seamlessly guarantee message delivery regardless of the network density (average number of neighbors per node), (2) easily incorporate any power-related optimization criterion to the routing protocol and (3) even target scenarios where both end nodes are actually disconnected from each other. Results gathered from extensive simulations argue for the introduction of the proposed hybrid framework.