We demonstrate the feasibility of long lasting underwater networking by proposing the smart exploitation of the energy harvesting capabilities of underwater sensor nodes. We define a data routing framework that allows senders to select the best forwarding relay taking into account both residual energy and foreseeable harvestable energy. Our forwarding method, named HyDRO, for Harvesting-aware Data ROuting, is also configured to consider channel conditions and route-wide residual energy, performing network wide optimization via local information sharing. The performance of our protocol is evaluated via simulations in scenarios modeled to include realistic underwater settings as well as energy harvesting based on recorded traces. HyDRO is compared to state-of-the-art forwarding protocols for underwater networks. Our results show that jointly considering residual and predicted energy availability is key to achieve lower energy consumption and latency, while obtaining much higher packet delivery ratio.