Promoting municipal solid waste (MSW) sorting is critical to advancing sustainable and low-carbon urban development. While existing research often focuses separately on external policy tools or internal behavioral drivers, limited attention has been given to their joint effects within an integrated framework. This study addresses this gap by analyzing micro-survey data from 1983 residents across 34 prefecture-level and above cities in China, using a bivariate probit model to examine how policy tools and policy perception—both independently and interactively—shape residents’ active and passive compliance with MSW sorting policies. The findings reveal five key insights. First, the adoption and spatial distribution of policy tools are uneven: environment-type tools dominate, supply-type tools are moderately deployed, and demand-type tools are underutilized. Second, both policy tools and policy perception significantly promote compliance behaviors, with policy cognition exerting the strongest effect. Third, differential effects are observed—policy cognition primarily drives active compliance, whereas policy acceptance more strongly predicts passive compliance. Fourth, synergistic effects emerge when supply-type tools are combined with environment-type or demand-type tools. Finally, policy perception not only directly enhances compliance but also moderates the effectiveness of policy tools, with notable heterogeneity among residents with higher cognitive or emotional alignment. These findings contribute to a deeper understanding of compliance mechanisms and offer practical implications for designing perception-sensitive and regionally adaptive MSW governance strategies.