In this paper, we study the problem of minimizing the uplink aggregate transmit power subject to the users' minimum data rate and peak power constraint on each sub-channel for multi-cell wireless networks. To address this problem, a distributed sub-optimal joint power and rate control algorithm called JPRC is proposed, which is applicable to both non-orthogonal frequency-division multiple access (NOMA) and orthogonal frequency-division multiple access (OFDMA) schemes. Employing JPRC, each user updates its transmit power using only local information. Simulation results illustrate that the JPRC algorithm can reach a performance close to that obtained by the optimal solution via exhaustive search, with the NOMA scheme achieving a 59\% improvement on the aggregate transmit power over the OFDMA counterpart. It is also shown that the JPRC algorithm can outperform existing distributed power control algorithms.