Recent Advances in Distributed Source Coding (DSC) motivate the mission-driven wireless sensor network application that relates to compression of multiple correlated sensor outputs, such as real time target tracking and environment monitoring. The characteristic of multiple rates in DSC applications requires the associated sensor network to support Rate-Oriented Routing (ROR) in order to extend the network life time. In this paper, we propose a novel optimal Rate-Oriented Routing based on the Distributed Energy Usage Scheduling (DEUS) for mission-driven DSC applications. The ROR adopts a new method called rate assignment instead of the traditional rate adaptation method in wireless networks to extend the network life time. The maximum network lifetime is achieved by constructing multiple rate-oriented paths between the source and sink, which balance the loads and lead to energy-efficient transmissions to meet the DSC application needs. Our simulation has shown that the Rate-Oriented Routing can extend the network life time and save energy significantly under the DSC application requirements.