Computational resources are increasingly virtualized to enable computational tasks to be offloaded to remote facilities along the route between the source and destination. The principle that underlies traditional routing, i.e., that only networking resources need to be considered, may no longer be true in a virtualized environment. In this paper, we propose a framework for the efficient utilization of multi-resource infrastructures in which computational resources can be used via the network. Such a framework intrinsically calls for the joint consideration of networking and computational resources. In particular, we focus on unifying the controls in dynamic service chaining and multiple resource management, which are the key technologies in an integrated SDN/NFV architecture. We formulate a multi-path problem for choosing the resources to use in different services. The problem can be viewed as variational inequality using the Lagrange duality and saddle point theory. Based on this, we develop an extragradient-based algorithm that controls and splits the sending rate of each service. We prove that the algorithm converges to the optimal, minimizing the system cost while maximizing service utility. Simulations for diverse scenarios demonstrate that our algorithm achieves high QoS while reducing the system cost by jointly considering dual-resource coupling and service characteristics.