The 3rd Generation Partnership Project (3GPP) standardized the NarrowBand Internet of Things (NB-IoT) technology in Release-13, aiming to support applications requiring minimal device power consumption, efficient small data transfer, and tolerance for delays. This paper provides two major contributions: first, it characterizes the NB-IoT architecture and its enhancements in subsequent 3GPP releases; second, it introduces an energy-saving technique for NB-IoT user equipment based on semi-Markov processes. Integrating a Proxy state and an enhanced release assistant indication (ERAI), the proposed technique improves upon the traditional Discontinuous Reception (DRX) method in the NB-IoT standard. This novel approach reduces energy consumption during low data communication, distinguishing it from other power-saving methodologies. The effectiveness of this technique is assessed through the power-saving factor (PSF) under various conditions, such as different eDRX durations (T_eDRX), PSM durations (T_PSM), DRX cycle periods (T_ACTIVE+T_SLEEP), and DRX active periods (T_ACTIVE). Our findings confirm that the proposed Proxy & ERAI technique significantly boosts the power-saving capabilities of NB-IoT devices, especially for small data packet transmissions. Theoretical and simulation results indicate that the PSF can be enhanced by up to 99.4% with optimized eDRX durations (T_eDRX) and up to 99.9% with optimized PSM (T_PSM) durations. These results underscore the significant energy-saving potential of our proposed technique, making it highly effective for NB-IoT applications with low data transmission needs.