(1) Background: Cognitive decline is associated with instrumental activities of daily living (IADL) disability. Intervention targeting the mediators of this association will provide a path to avoid cognition-related IADL disability. (2) Methods: This study used data of wave 2008 (baseline) and wave 2014 of Chinese Longitudinal Healthy Longevity Surveys. Structural equation modeling was conducted to examine the mediating effect of social interaction, lifestyle (fruit and vegetable intake; exercise habits), and depressive status on the association between four baseline cognitive function dimensions (measured by the Chinese version of the Mini-Mental State Examination) and five (2014) IADL dimensions (visiting neighbors, shopping, preparing meals, washing clothes, and taking public transportation). (3) Results: Among 1976 older adults, 29.1% developed IADL disability 6 years later. The cognition–disability association was completely mediated by social interaction (estimate = −0.095, p < 0.001), lifestyle (estimate = −0.086, p < 0.001), and depressive status (estimate = −0.017, p = 0.003). The mediating effects of social interaction (46.3% variances explained) and lifestyle (42.0% variances explained) were both larger than that of depressive status (8.3% variances explained). (4) Conclusions: The development of interventions aimed at improving social interaction, depression, and lifestyle could be of value to prevent cognition-related IADL disability.