Branded applications (apps) became a new trend in mobile marketing because they offer a better way to capture on-the-go consumers. This study thus explores how to promote app users’ continuance intention and purchase intention (i.e., “app continuance”) toward a specific branded app. By integrating service-dominant (S-D) logic and task-technology fit, this study utilizes a unifying model to examine how task-service fit (TSF) influences app continuance. This study identifies task characteristic and four service characteristics (interactivity, presence, localization, and ubiquity) as antecedents of TSF. Psychological barriers are examined as mediators of TSF and purchase intention within S-D logic. Data collected from 631 users of the targeted branded apps support all of the proposed hypotheses. The findings show that TSF is an essential determinant of both app continuance in the context of branded apps and a partial mediator of psychological barriers between TSF and purchase intention. The results provide new perspectives for designers and marketers of branded apps on how to create better service experiences for their customers.