Background/Objectives: This study investigates consumers’ purchase intention (PI) toward health and wellness foods (HWF) in China by examining key factors, such as health-consciousness (HC), desire, and attitude toward organic food. Methods: Data were collected via online surveys completed by Chinese respondents aged 50–65 years. Of the 270 distributed surveys, 230 valid responses (85.2% effectiveness) were analyzed. A multi-analytic approach was employed, integrating Partial Least Squares–Structural Equation Modeling (PLS–SEM), Necessary Condition Analysis (NCA), and Combined Importance-Performance Map Analysis (cIPMA), to explore the hypothesized relationships. Results: The results reveal consumers’ HC has a strong influence on their PI toward HWF, with attitude and desire sequentially mediating this relationship. Furthermore, the results of NCA confirm that HC and desire are necessary conditions for purchasing HWF, whereas attitude is not. Conclusions: Based on these findings, the study provides suggestions for future research and practical recommendations for HWF businesses.