In this paper, we formulate a network utility maximization (NUM) problem, targeting an optimal cross-layer network operation, while considering time-varying and random possibly non-stationary wireless channels. As indicated in the literature, this problem imposes scalability constraints when the time horizon of the network control increases, impeding an online (i.e., real-time) application of its solution during the network operation. To achieve an online network control, in this paper, we leverage on model predictive control (MPC) or receding horizon control (RHC) for the solution of the NUM problem. Furthermore, MPC/RHC allows for the adaptation of the optimal controls in dynamic and evolving network conditions, in our case with respect to the wireless channels, the modeling parameters of which are estimated in an online fashion. We present and analyze the NUM problem, while we appropriately reformulate it for applying MPC/RHC. Then, we describe the MPC/RHC-based algorithmic solution, which determines the decisions for the online network control including power control, scheduling, routing, and congestion control, while we discuss stability and optimality issues. Finally, we evaluate the proposed methodology via numerical results and we show that the performance lies very close to the optimal one even for relatively small receding horizon lengths that significantly reduce the computational time complexity.