Carrier-sense multiple access with collision avoidance (CSMA/CA) is one of the fundamental medium access control (MAC) protocols for ad hoc networks. As a network’s size increases, its throughput degrades substantially because of packet collisions. To reduce the collision probability, combining non-orthogonal multiple access (NOMA) with CSMA/CA is a promising solution. However, existing NOMA-CSMA/CA protocols adopt distributed power selection and channel inversion power control, resulting in a high power collision probability and limiting the number of power levels. To address these issues, we propose a power back-off NOMA-based CSMA/CA (PBN-CSMA/CA) protocol for ad hoc networks. The proposed protocol achieves centralized power allocation, avoiding power collisions by employing the Zadoff-Chu (ZC) sequence and the power level allocation (PLA) frame. Additionally, power back-off (PB) control is used to set the transmission power, which expands the number of power levels and gives full play to the performance advantages of NOMA. To analyze the performance comprehensively, the closed-form expressions of the average outage probability, normalized saturation throughput, average packet delay and transmission energy consumption are theoretically analyzed. Both the analytical and simulation results demonstrate that the PBN-CSMA/CA protocol outperforms the existing NOMA-CSMA/CA and traditional CSMA/CA protocols, with significant throughput gains and delay reductions.