Objective: Grounded in the Unified Theory of Acceptance and Use of Technology (UTAUT), this study aims to examine patients’ behavioral intention (BI) toward accepting electroacupuncture analgesia and identify key determinants that influence its adoption. Methods: We conducted a multicenter cross-sectional study with questionnaire-based data collection and analyzed associations using structural equation modeling (SEM). Reporting followed the STROBE guidelines. Results: A total of 325 participants were included in the analysis. Performance expectancy (PE) (β = 0.272, p < 0.001), effort expectancy (EE) (β = 0.610, p < 0.001), and facilitating conditions (FC) (β = 0.586, p < 0.001) exhibited significant positive effects on BI. Social influence did not exert a significant effect (β = 0.217, p = 0.090). FC had a significant negative effect on use behavior (UB) (β = −0.617, p < 0.001), forming a competitive mediation model with its positive indirect effect via BI. Significant differences in BI were observed across participants of different age groups, social backgrounds, educational levels, occupations, and income levels (p < 0.05). The model exhibited a good fit, supporting the applicability of the theoretical framework. Conclusion: EE, PE, and FC are key factors influencing patients’ acceptance of electroacupuncture analgesia. FC exhibited a competitive mediation effect on UB, highlighting the necessity of optimizing convenience conditions to meet the higher expectations of experienced users. Future initiatives should focus on developing tailored strategies for diverse demographic groups to enhance the clinical adoption and therapeutic effectiveness of electroacupuncture technology.