High-throughput satellite (HTS) is viewed as a promising solution for the next generation of satellite-based Internet of Things (S-IoT). Considering that the onboard communication resources, such as power and storage, are limited, we formulate a joint network stability and resource allocation optimization problem to maximize the long-term network utility of a nonorthogonal multiple access (NOMA) S-IoT downlink system. First, we establish two virtual queues for both the data queueing and power expenditure. Then, a joint optimal problem can be formulated as a problem that optimizes the time average of network utility, which perfectly matches the Lyapunov optimization framework. Therefore, by taking into account the condition of successive interference cancellation decoding, we propose a practical solution under the Karush–Kuhn–Tucker (KKT) conditions, and further introduce an optimal solution by using the particle swarm optimization (PSO) algorithm for the joint resource allocation problem. The simulation results demonstrate that our joint optimization allocation schemes outperform the existing benchmark schemes.