Green innovation is an important driver for the sustainable development of the real economy and the realization of a green transformation. Previous studies have paid less attention to the relationship between dividend payments and the persistence of green innovation and neglected the mechanism of knowledge management on the relationship between the two. Using Chinese listed non-financial companies from 2007 to 2022, this paper empirically investigates the effect and mechanism of dividend payment on corporate green innovation persistence based on two perspectives: principal–agent theory and incentive theory, using Tobit and negative binomial models. It was found that there is a non-linear inverted U-shaped relationship between dividend payments and the persistence of green innovation. Dividend payments influence the persistence of green innovation through agency costs and knowledge management capabilities. Both independent director networks and knowledge spillovers have a positive impact on the relationship between the two. Based on firms’ characteristics, the inverted U-shaped relationship between dividend payment and green innovation persistence is found to be more significant for non-state-owned firms and high-tech firms. Depending on the shareholder type, the inverted U-shaped curve between dividend payments for shareholding managers and green innovation persistence is the steepest. This study enriches the relevant literature on green innovations. In addition, it provides companies with a reference for formulating appropriate dividend policies, improving knowledge management capabilities, and improving the persistence of green innovation at a firm level.