The demand for mobile uplink traffic has increased significantly in the past few decades with the development of the Internet of Things (IoT) and mobile Internet. This has subsequently imposed challenges on 5G networks to provide high spectral efficiency and low-power massive connectivity. Non-orthogonal multiple access (NOMA) is a viable alternative to the current state-of-the-art orthogonal multiple access (OMA) techniques to address the challenges in 5G systems. In addition, a power control (PC) mechanism to mitigate the effect of interference between users can be accommodated to improve network performance. In this paper, we discuss the basic principles, key features, and strengths/weaknesses of the various power domain NOMA schemes. Moreover, we propose an uplink PC scheme for the users of a power domain NOMA network. The proposed PC method makes use of the evolutionary game theory (EGT) model to adaptively adjust the transmitted power level of the users which helps in mitigating user interference. A successive interference cancellation (SIC) receiver is applied at a base station (BS) in order to separate the users’ signals. By performing simulations, we show that the proposed EGT-based PC scheme achieves higher network efficiency, spectral efficiency, and energy efficiency.