Driven by the ever-increasing computing capabilities of mobile devices, the next-generation wireless networks are evolving towards distributed networking and computing platforms, which enable in-network computing and unified resource/service provisioning. The evolution leads to a growing research interest in wireless computing networks that operate under the high dynamics of the wireless environment, the complexity of heterogeneous resource allocation, scheduling, and overall optimization. In this paper, we propose a low-complexity efficient solution to jointly allocate both networking resources (e.g., links to forward packets between connected computing nodes) and computing resources (e.g., computing power at each node for packet processing) for wireless computing networks. Specifically, we propose a novel network utility maximization problem under computing and networking resource constraints and develop an enhanced backpressure-based dynamic scheduling and routing algorithm. We verify the network stability and near-optimal performance of the algorithm via both theoretical analysis and extensive simulations.