Since the non-orthogonal multiple access (NOMA) with successive interference cancellation (SIC) can achieve superior spectral-efficiency and energy-efficiency, the concept of SCN using NOMA with SIC is proposed in this paper. Due to the difference of small-cell base stations’ locations, each mobile user perceives different channel gains to different small-cell base stations. Therefore, it is important to associate a mobile user with the right base station and control its transmit power for the uplink SCN using NOMA with SIC. However, the already-challenging base station association problem is further complicated by the need of transmit power control, which is an essential component to manage co-channel interference. Despite its importance, the joint base station association and power control optimization problem that maximizes the system-wide utility and at the same time minimizes the total transmit power consumption for the maximum utility has remained largely unsolved for the uplink SCN using NOMA with SIC, mainly due to its non-convex and combinatorial nature. To solve this problem, we first present a formulation transformation that captures two interactive objectives simultaneously. Then, we propose a novel algorithm to solve the equivalently transformed optimization problem based on the coalition formation game theory and the primal decomposition theory in the framework of simulated annealing. Finally, theoretical analysis and simulation results are provided to demonstrate that the proposed algorithm is guaranteed to converge to the global optimal solution in polynomial time.