In the past decade, as more and more passengers choose to fly on trips, China’s airport infrastructure construction has achieved world-renowned achievements. Despite the growing opportunities and demands for using brand research to assist airport industry services in improving, few studies have investigated the impact of service quality in terminal facilities on brand due to the diversity of service. This study uses structural equation models based on empirical research to explore the impact of facility service quality, including processing facility and non-processing facility, on airport brand experience and passenger satisfaction. This study also aims to assess the mediating effect of brand engagement on the relationship between facility service quality, brand experience, and passenger satisfaction. At the same time, this study also uses importance–performance map analysis (IPMA) to find specific items influencing brand engagement. The sampling method used a random sampling approach, with a total of 186 questionnaires distributed at Shanghai Pudong International Airport for data analysis. The results show that airport facility service quality is significant for brand engagement and experience, as well as for satisfaction, especially for processing facilities. In addition, the IPMA results show that facility services involved in the check-in process is of high importance, which requires more attention from managers. Overall, the findings of this study extend the understanding of service quality, brand engagement, brand experience, and passenger satisfaction in the context of an international airport, and they offer implications for Shanghai Pudong International Airport regarding the improvement of its facilities and brand.