Networked control systems (NCS), such as the smart power grid, implement feedback control loops by connecting distributed sensors and actuators to a remote controller over a communication network. In order to avoid the costly and time-consuming installation of dedicated networks, NCS can benefit from utilizing readily available IP networks such as the Internet. However, as control systems are typically sensitive to delay and loss, the integration of such systems over best-effort networks becomes a challenge, which we address in this paper with two main contributions. First, we propose an end-to-end transport abstraction for NCS based on a novel probabilistic quality of service specification which (1) is compatible with existing control models and (2) provides the network with application-specific knowledge about the relation between system performance and network-relevant metrics. Second, we realize this abstraction at the network layer with an optimal routing algorithm, which fulfils the required QoS while minimizing the usage of network resources. We show that our approach lends itself to the implementation with state-of-the-art software-defined networking (SDN) technologies, and demonstrate its effectiveness in our evaluation.